10 I beseech thee for my son Onesimus, whom I have begotten in my bonds:
[AD 380] Apostolic Constitutions on Philemon 1:10
Of Borea in Macedonia, Ones Imus, once the servant of Philemon.

[AD 384] Ambrosiaster on Philemon 1:10
During his imprisonment in Rome, the apostle had baptized Onesimus, a runaway who had fled to God for help, because he saw Onesimus's potential.
[AD 407] John Chrysostom on Philemon 1:10
For I would not have called him my son, Paul says, if he were not of great use and importance to me. What I called Timothy, that I also call Onesimus. Paul repeatedly shows his affection for Onesimus, reminding Philemon of Onesimus’s recent birth in Christ. “I have begotten him in my bonds,” he says, so that also on this account Onesimus was worthy to obtain much honor, because he was begotten in Paul’s very conflicts, in his trials in the cause of Christ.

[AD 407] John Chrysostom on Philemon 1:10
And note, on the other hand, also Paul’s fervency. He preached the gospel bound and scourged. Oh, that blessed chain, with what great effort did it labor that night, and what children did it birth! Yes, of them, too, may he say, “Whom I have begotten in my bonds.” Observe how Paul glories. He will have the children born this way considered even more illustrious! Observe how transcendent is the glory of those bonds, in that they give luster not only to him that wore them but also to those who were on that occasion begotten by him.

[AD 420] Jerome on Philemon 1:10-13
"I beseech you concerning my son, whom I have begotten in chains, Onesimus, who was once useless to you, but is now useful to both you and me, whom I have sent back to you. But you, receive him, that is, my own heart, whom I wished to keep with me, so that he might serve me on your behalf in the chains of the gospel. " In wishing to obtain what he asks for, he now asserts that he is pleading not for Philemon's slave, but for his own son. And regarding that son whom he has begotten in the chains of the gospel, that is, which he endured for the sake of Christ's gospel: who, although he was once useless to his master (for a slave who steals and runs away harms no one but his own master), now on the contrary, by way of compensation for his usefulness to both his master and Paul, and to others through Paul, he deserves more love than he had previously deserved hatred. He says, "Who was useless to you at one time." "To you alone," he says, "not to others: but now it is useful to both me and you." It is useful to the master in that he could serve Paul as his master; Paul, however, is useful in this: that he could minister to him in the Gospel while he was being held in prison and chains. And at the same time we admire the magnanimity of the apostle and his fervent mind in Christ. He is held in prison, is bound in chains, is oppressed by the filth of his body, by separation from his loved ones, is cramped by penal darkness, and yet he feels no wrong, he is not tortured by pain, he knows nothing else but to think about the Gospel of Christ. He knew the slave, he knew the fugitive, he knew that he had been converted to the faith of Christ by a kidnapper. It is a great effort for a man to persevere in what he has begun. Therefore, he impresses, repeats, and urges his son and the son of bonds, and minister of the Gospel who is imprisoned, that Philemon, praised only in the preface, would not dare to refuse, lest he appear unworthy of his own praises. And what he says: "But you accept him, that is, my heart," this is what I said a little earlier, that "heart" signifies the internal affection of the heart and the full willingness from the soul, when everything that is in us is received from the one asking. But otherwise, all children are the parents' hearts.

[AD 428] Theodore of Mopsuestia on Philemon 1:10
Now Paul uses the name of Onesimus, but only after signaling the profound change that has occurred [i.e., Onesimus’s conversion].

[AD 749] John Damascene on Philemon 1:10
Indeed the epistle was written in behalf of the slave, and having returned him, though he had done wrong, he was improving through the Apostle's teaching. Now many have benefitted from it, indeed, first and foremost those who are zealous. For if Paul makes such great haste for the fugitive and repentant thief, how much more shall we not be lazy for the brethren. Secondly, one must not give up on the servile class, even if it strains the uttermost limits of wickedness. Oh how the thief and fugitive became so virtuous! Thirdly, its not appropriate for slaves to run away from their masters. For if Paul now insures Philemon that Onesimus was now thankful to serve him and not wishing to defy his superior, how much more should we ought not to do it. For if the wonderful servant is still fit to remain in his job, and their masters realize it, then he may be useful in everything else in the household.
[AD 1274] Thomas Aquinas on Philemon 1:10
Therefore he says, I plead with you for my own son, whom I have begotten in prison, for Onesimus, who is his present concern. And acquiring a son in default of time, he loves him more, as an old man loves sons born to him in his old age. Genesis 37:3: ‘Now Israel loved Joseph above all his sons, because he had him in his old age.’ This one [Onesimus] was given birth in chains. Second, there is the change in status. For if he had persevered in sin, he would not be worthy of leniency. Note that Paul says little and means much. For as Cicero taught, one ought to make little of one’s own deed as much as possible. Thus the Apostle speaks lightly of his offence, saying, He once was useless to you, that is, harmful in taking away your possession, but now, converted from evil to the state of virtue, he is useful for the service of God and man. 2 Timothy 2:21: ‘If anyone, therefore, has cleansed himself from these, he will be a vessel for honourable use...’ Proverbs 25:4: ‘Take away the rust from silver, and there shall come forth a most pure vessel.’