en_tn/php/02/22.md

Timothy has proven himself

What Timothy has proven about himself can be made explicit: "Timothy has shown that he cares about the things of Christ" (See: rc://en/ta/man/translate/figs-explicit).

as a child serves his father, so he served with me

Paul compares Timothy's service with him to a child serving his father. Paul is emphasizing the close father-son relationship he has with Timothy in serving Christ. (See: rc://en/ta/man/translate/figs-simile)

in the spread of the gospel

"in telling people about the gospel"

I am confident in the Lord, that I will come soon

This could be translated as "I am sure, if it is the Lord's will, that I will come soon."