"my son Onesimus." Paul speaks of the way he is friends with Onesimus as if it were the way a father and his son love each other. Onesimus was not Paul's actual son, but he received spiritual life when Paul taught him about Jesus, and Paul loved him. AT: "my spiritual son Onesimus" (See: [[rc://en/ta/man/translate/figs-metaphor]])
Here "fathered" is a metaphor that means Paul converted Onesimus to Christ. AT: "who became my spiritual son when I taught him about Christ and he received new life while I was in my chains" or "who became like a son to me while I was in my chains" (See: [[rc://en/ta/man/translate/figs-metaphor]])
Prisoners were often bound in chains. Paul was in prison when he taught Onesimus and was still in prison when he wrote this letter. AT: "while I was in prison ... while I am in prison" (See: [[rc://en/ta/man/translate/figs-metonymy]])
"Heart" is a metonym for inner life, or "motivation for living." AT: "who is my very motivation for living" (See: [[rc://en/ta/man/translate/figs-metonymy]]).
Paul was in prison because he preached the gospel publicly. This can be stated explicitly. AT: "because I preach the gospel" (See: [[rc://en/ta/man/translate/figs-explicit]])