en_tn/php/02/22.md

as a son with his father, so he served with me

Fathers and sons love each other and work together. Timothy was not really Paul's son, but he worked with Paul as a son works with his father. (See: rc://en/ta/man/jit/figs-simile)

in the gospel

Here "the gospel" stands for the activity of telling people about Jesus. Alternate translation: "in telling people about the gospel" (See: rc://en/ta/man/jit/figs-metonymy)