Here "child" is a term of great love and approval. It is also likely that Timothy was converted to Christ by Paul, and so this is why Paul considered him like his own child. Alternate translation: "who is like my child" (See: [[rc://en/ta/man/jit/figs-metaphor]])
Paul speaks about the motivation and determination that God's grace allows believers to have. Alternate translation: "let God use the grace he gave you through your relationship to Christ Jesus to make you strong" (See: [[rc://en/ta/man/jit/figs-metaphor]])