Be remaining in (Literal),
abide thou in (ASV),

see that you keep to, continue to hold (Amp),

you must keep to what you have been taught (NJB),

 you must cling to what you have learnt (Weymouth)

you must go on steadily (Phillips),

remain loyal to the things which you have learned (Barclay)

be remaining ..in (Wuest)

In the preceding section Timothy has been warned about guaranteed persecution and deepening deception so that he might be prepared to endure hardship and to fulfill his ministry. In these last 4 verses Paul reminds Timothy that his ultimate source of power to stand firm will come from the Scriptures learned, shown to be reliable and sufficient in the lives of those who had taught him (3:14, 15) and firmly grounded in the fully inspired Word of God (see notes 2 Timothy 3:16; 3:17).

You however in the NASB softens the Greek which is more accurately rendered But you which sets up an emphatic contrast with the evil men just described.

However then stands in contrast to the many who will plunge deeper and deeper into the cesspool of deception and darkness (see note 2 Timothy 3:13 and 2 Timothy 3:2ff), Timothy is to stand firm on the solid rock of God's unchanging word. This verse begins with the emphatic you (su) which we last saw in (see note 2 Timothy 3:10). The man of God must pay careful attention to himself and the Scriptures if he is to resist the enticing lure of doctrinal infidelity. As opposition increases, the Scriptures become the believer’s reliance and bulwark.

Proverbs reminds us that

EVERY WORD of God (the Scriptures) is tested. He is a shield to those who take refuge in Him. (Pr 30:5)

Peter adds that

His divine power has granted to us EVERYTHING pertaining to life and godliness, through the TRUE KNOWLEDGE (in the Scriptures) of Him (Jesus)" and "He has granted to us His PRECIOUS and MAGNIFICENT PROMISES (in the Scriptures), in order that by them you might become partakers (sharers) of the divine nature. (see notes 2 Peter 1:3; 1:4).

As Hiebert emphasizes

The remembrance of Paul's heroic sufferings (see notes 2 Timothy 3:10; 3:11), as well as the realization that suffering is the lot of all believers (see note 2 Timothy 3:12), will undergird Timothy's endurance. But the ultimate source of his power to stand firm he must find in the Scriptures. Paul reminds him of his subjective experience with the SACRED WRITINGS (2 Timothy 3:14  3:15) and asserts the objective fact of the nature and function of the SCRIPTURES (see notes 2 Timothy 3:16; 3:17). (caps added)

Continue (3306) (Meno) means to abide or remain in the same place over a period of time. The present imperative calls for a constant, habitual way of life. Timothy is to be a "man of the Book" and thereby armed against the snares and insinuations of seducers. In light of the deepening degradation of these self-willed deceivers it is imperative that Timothy firmly adhere to the divine truth he had previously heard and accepted. Thus Paul commands Timothy to continually abide in the Truth he had learned. Dwell in it and live in it and do not "proceed" or "advance" away from it like the false teachers. To continue however means more than merely continuing in orthodoxy. It calls for a commitment to live and abide in what Timothy had learned. Why? Because it is your very life! (Dt 32:47).

All true progress must be within not away from the fundamentals of the faith found only in the faithful Word. Are you wondering about or wandering from the "word of truth" (see note 2 Timothy 2:15)?

Are you reading or listening to liberal pastors or teachers who are adding to or taking from the complete revelation of divine Truth? Then run, flee for your spiritual life and

pay close attention to yourself and to your teaching; persevere in these things; for as you do this you will insure salvation both for yourself and for those who hear you. (1Ti 4:16) and

retain the standard of sound words which you have heard from me. (see note 2 Timothy 1:13).

How precious that in his childhood, Timothy was given something to continue in! 

Are you giving your children the "gift that keeps on giving?"

Kelly translates continue as stand by commenting that

Perhaps one of the severest tests of a believer's character and loyalty is to "stand by" the side of known truth while alluring and scintillating heresies are paraded in front of us. It is no small feat to remain faithful to God's eternal word throughout one's lifetime and many there are who have left its ranks." Or as God says to wayward Israel through the prophet Jeremiah "Stand by the ways and see and ask for the ancient paths, where the good way is, and walk in it; and you shall find rest for your souls. (Jer 6:16)

Mt Henry has an excellent reminder for all "young Timothys":

It is not enough to learn that which is good, but we must continue in it, and persevere in it unto the end. Then are we Christ’s disciples indeed," (Jn 8:31). (bolding added)

Oswald Chambers exhorts us writing...

Am I learning how to use my Bible? The way to become complete for the Master’s service is to be well soaked in the Bible, some of us only exploit certain passages. Our Lord wants to give us continuous instruction out of His word; continuous instruction turns hearers into disciples. Beware of “spooned meat”* spirituality, of using the Bible for the sake of getting messages; use it to nourish your own soul. Be a continuous learner, don’t stop short, and the truth will open to you on the right hand and on the left until you find there is no problem in human life with which the Bible does not deal. But remember that there are certain points of truth Our Lord cannot reveal to us until our character is in a fit state to bear it. The discernment of God’s truth and the development of character go together. The life God places in the Christian worker is the life of Jesus Christ, which is continually changing spiritual innocence into glorious practical character. (Complete for the Master’s Service - Approved unto God)

Brothers and sisters let us press on for the prize (see note Philippians 3:14) and

no longer to be children, tossed here and there by waves, and carried about by every wind of doctrine"  (see note Ephesians 4:12) and

Do not be carried away by varied and strange teachings; for it is good for the heart to be strengthened by grace" (see note Hebrews 13:9)  

Hall echoes the charge that...

God’s servants must continue constant in the truth received. They must not play fast and loose, be off and on; but they must be still the same, like well-tuned bells, which have the same note in foul weather as they have in fair"(Job 1:21) (T. Hall, Biblical Illustrator)

Clarke (critique) adds a note on the importance of continuing in the truth:

No man, however well instructed in the things of God, or grounded in Divine grace, is out of the reach of temptation, apostasy, and final ruin; hence the necessity of watching unto prayer (Mt 26:41), depending upon God (2Cor 3:5, 3:6, 12:9, 12:10, see notes Philippians 4:13, Colossians 1:11), continuing in the faith (see note Colossians 1:23) , and persevering unto the end (Mt 24:13 Lu 8:15, see note Hebrews 3:6).

As Paul reminded Timothy, many others did not continue but went "straying" (1Ti 1:6), "suffered shipwreck" (1Ti 1:19), had "gone astray" (1Ti 6:20), had "turned away" (see note 2 Timothy 1:15), "deserted" (see notes 2 Timothy 4:10; 4:16).

If you preserve the truth it will preserve you in the hour of temptation (cf Pr 4:8),

><> ><> ><>

Standing or Falling? from Our Daily Bread - Part of the training to be a US Secret Service agent includes learning to detect counterfeit money. Agents-in-training make a thorough study of the genuine bills--not the phonies--so that they can spot the fake currency immediately because of its contrast to the real thing. The child of God can learn a lesson from this. While it is helpful to study false religions and be fully aware of their dangerous dogmas, the best defense against such error is to be so familiar with God's Word that whenever we encounter error, we will spot it at once and won't fall for it. Today many are being led astray because they don't recognize how they are being deceived. For example, if a person isn't solidly grounded in the teaching of salvation by grace, he may swallow the line of the legalists who inject human works into the matter of being saved. If he is not well instructed about the person of Christ, he might accept the error of those who deny the Savior's deity. A thorough knowledge of essential biblical doctrines is the only way to detect counterfeits. Let's be diligent in our study of the Word of God. Then, instead of falling into error, we will stand firmly on the truth. --RWD

IN THE THINGS YOU HAVE LEARNED: en hois emathes (2SAAI) :

Learned (3129) (manthano - TDNT says is derived from a root meaning to direct one's mind to something) has a basic meaning of to learn with the idea being to gain knowledge by instruction or to come to understand as the result of a process of intentional inquiry and observation. The aorist tense speaks of a historical fact, a past completed event - he had learned indeed learned these things.

Manthano is related to the Greek word for disciple (mathetes = learner, pupil) referring to one (like Timothy) who puts himself under the teaching of someone else (like Paul) and learns from him. The aorist tense identifies the "learning" as a past completed action (historical event). John had a similar thought -

These things I have written to you concerning those who are trying to deceive you. (1Jn 2:26)

The best antidote for deception is the truth of God's Word is the "things you have learned". This was true for Timothy then and it is just as true for you and I today in a time when even supposed bastions of the Truth such as many seminaries and pulpits are departing from the sufficiency "pure milk of the Word". (see note 1 Peter 2:2)

It is a blessed state to

know the exact truth about the things you have been taught. (Lu 1:4)

Mt Henry adds that it is important

not only to know what the truths are, but to know that they are of undoubted certainty. What we have learned we must labour to be more and more assured of, that, being grounded in the truth, we may be guarded against error, for certainty in religion is of great importance and advantage

AND BECOME CONVINCED OF: kai epistothes (2SAPI): (cf 1Cor 15:1, 15:2)  (Acts 17:31; Ro 14:5; Col 2:2; 1 Thes 1:5; Heb 6:11; 10:22)
 

and are confident about (NET)

and which you know are true (Phillips)

and know to be true (NJB)

and have been assured of (Wuest)

and have firmly believed (ESV)

and found to be true (GWT)

things of which you are certain (BBE)

of which thou hast been fully persuaded (Darby)

and your belief that has been confirmed (Barclay)

Become convinced (4104) (pistoo from pistós =  faithful) means assured, made certain and the aorist tense identifies that a past completed action (historical fact). Timothy not only learned the great truths of the faith, but he had become personally assured of them as well. Timothy had an inner conviction concerning the truth and reliability of these things and such confidence produces personal stability. Without this conviction of heart, it would have been difficult for Timothy to hold fast in the things he had learned amid so many persecutions and deceptions.  

Hiebert adds that on the other hand

doubts and uncertainties concerning the Word of God never foster moral steadfastness.

KNOWING FROM WHOM YOU LEARNED: eidos (RAPMSN) para tinon emathes (2SAAI): (see note 1Thessalonians 2:13)

You know they are true, for you know you can trust those who taught you. (NLT)

Remember from what sort of people your knowledge has come (Phillips)

Knowing (1492) (eido) refers to absolute, positive, beyond a doubt knowledge. It means to see with the mind’s eye and signifies a clear and purely mental perception. The perfect tense speaks of the permanent or abiding state of Timothy's knowing.  The Scriptures had been taught to him by those whose lives witnessed to the reality of their faith.  Timothy knew that Paul was imprisoned for the sake of the gospel, and that the gospel was not just worth living for but worth dying for.

Whom is a plural pronoun (less reliable manuscripts have singular) which would include the OT prophets ("speaking" through the Scripture), Timothy's grandmother Eunice, his mother Lois (see note 2 Timothy 1:5), and his mentor Paul (see note 2 Timothy 1:13, 2:2, 3:10). To successfully learn spiritual convictions from others and to hold them as your own, it is necessary not only to hear them clearly taught but to see them consistently lived. In other words, although the content of the teaching is obviously of critical importance so too is the character of the teacher ("you followed my teaching, conduct...3:10').

Learned (3129) (see manthano above)

Timothy's personal knowledge of his teachers assured him of the reliability of the things he has learned. Writing to the new converts in Thessalonica Paul said

you know what kind of men we proved to be among you for your sake (see note 1Thessalonians 1:5).

Similarly, in his parting challenging exhortation to the Ephesian elders Paul said

You yourselves know, from the first day that I set foot in Asia, how I was with you the whole time, serving the Lord with all humility and with tears and with trials which came upon me through the plots of the Jews; how I did not shrink from declaring to you anything that was profitable.... (Acts 20:18 20:19 20:20).

So we see Paul continually backing up the words of his lips with the works in his life, a profitable practice for all believers to continually strive to imitate (1Cor 11:1)

Note the important distinction Paul makes, as "things learned" refers primarily to CONTENT, whereas things Timothy had "become convinced of" refers to CONVICTION. Timothy had not only "learned" the truth, but he had "become convinced" of it. "Convinced" is used in secular Greek writings to describe a theory or hypothesis which one had confirmed. You might be asking "So what is the significance of the things we "learn" and those we "become convinced of"? Succinctly stated -- We hold the former while the latter holds us!

from infancy (NET)

from a babe (ASV, Young's Literal)

a very young child (Wuest)

Childhood (1025) (brephos) meant a babe and in classical Greek referred to a babe at the breast. Thus the idea is literally “from infancy.” Peter uses the same term to exhort his readers to

like newborn babes, long for the pure milk of the word, that by it you may grow in respect to salvation (see note 1 Peter 2:2)

It was at the knees of his “grandmother Lois, and [his] mother Eunice” (see note 2 Timothy 1:5) that Timothy appears to be led to saving faith, and it was in their lives that he first saw the power of the gospel to produce genuine godliness. By Jewish custom children were taught God's Law at a very early age, and were encouraged to commit it to memory.

Barclay (critique) adds that

It was the glory of the Jews that their children from their earliest days were trained in the law. They claimed that their children learned the law even from their swaddling clothes and drank it in with their mother’s milk. They claimed that the law was so imprinted on the heart and mind of a Jewish child that he would sooner forget his own name than he would forget it.

Have known (1492) (oida) is perfect tense and conveys that idea that Timothy's knowledge of the "Sacred Writings" began in earliest childhood and continues through the present time. He cannot recall a period when he had not known the sacred writings.

Mt Henry adds that

The age of children is the learning age; and those who would get true learning must get it out of the scriptures.

In Timothy's case the teaching was clearly effectual for "true learning". May all Scriptural teaching to young ones be so effectual.

Albert Barnes adds that...

The Jewish writings abound with lessons on this subject. Rabbi Judah says, “The boy of five years of age ought to apply to the study of the sacred Scrip