A.T. Robertson Commentary Philemon 1:10

"I beseech thee for my child, whom I have begotten in my bonds, Onesimus," — Philemon 1:10 (ASV)

For my child (περ του εμου τεκνου). Tender and affectionate reference to Onesimus as his spiritual child.

Whom I have begotten in my bonds (ον εγεννησα εν τοις δεσμοις). First aorist active indicative of γενναω, to beget. See 1 Corinthians 4:15 for this figurative sense. Paul is evidently proud of winning Onesimus to Christ though a prisoner himself.