But you know Timothy's proven worth, how as a son with a father he has served with me in the gospel. (Philippians 2:22, ESV)There is something to be said for the love that can develop between two men. Timothy has served Paul like a loving son would. Timothy isn't his son in reality, though one might argue that Timothy is his son in the faith. The point is that these two men have served, side-by-side. In this case, not like brothers, but like a father and son. Timothy has shown himself worthy to Paul. Paul is now telling the Philippian church that they can trust Timothy to be there in Paul's place.
For what is our hope or joy or crown of boasting before our Lord Jesus at his coming? Is it not you? (1 Thessalonians 2:19 -- ESV) Three things mentioned here... "hope" ... "joy" ... "crown of boasting" ... Hope - What does Paul have his sights set on? Joy - What is it that brings Paul joy? Crown of Boasting - That Olympic Wreath of Glory that is placed on his head? It is these people. It is his children in the faith. They are Paul's Hope and Joy and Crown of Glory when Jesus returns.