Philippians 2:22 (ESV)

22 But you know Timothy’s proven worth, how as a son with a father he has served with me in the gospel.

Now Paul involves the Philippians in this: don’t they themselves have positive experiences with Timothy? They know of his proven loyalty—probably already from the early days of this church, though this is not explicitly mentioned in Acts 16:1–40. In any case, Timothy has already worked together with Paul for such a long time, that the members of the church know very well how loyal Timothy is, and how he worked as a son with his father.

Timothy is much younger than Paul. Even in a later letter, Paul writes to Timothy about his youthful age (1 Timothy 4:12). In 1 Timothy 4:12 and also in 2 Timothy 1:2, Paul, as a father, calls Timothy his child. Timothy has served in the gospel as a slave—not as a slave of Paul, but together (with me) they served Christ.