en_tn_condensed/phm/01/04.md

I thank my God always, making mention of you in my prayers

"When I pray for you, I always thank God (UDB).

I

Paul wrote this letter. The words "I" and "me" in this letter all refer to Paul.

you

Here and in most of the letter, the word "you" refers to Philemon. (See: rc://en/ta/man/translate/figs-you)

that your participation in the faith may be effective for the knowledge

This could also be translated as "that your trusting in Christ as we do will make you able to know" or "that because you joined us in trusting in Christ, you will be able to know"

your participation in the faith

"because you trust in Christ the same as we do" (UDB)

that is in us in Christ

The most likely meaning is "that we have because of Christ."

the hearts of the saints have been refreshed by you

Here the word "hearts" refers to the courage of the believers. Also, "have been refreshed" is a passive clause. This could be translated as an active clause: "you have encouraged the believers." (See: rc://en/ta/man/translate/figs-metonymy and rc://en/ta/man/translate/figs-activepassive)

brother

Paul called Philemon "brother" because they were both believers. He was also probably emphasizing their friendship. It can also be translated here as "dear brother" or "dear friend."