1 Grk “Paul.” The word “from” is not in the Greek text, but has been supplied to indicate the sender of the letter.
2 The phrase a prisoner of Christ Jesus implies that Paul was being held prisoner because of his testimony for Christ Jesus. Paul’s imprisonment was due to his service to Christ, in the same manner as John was exiled to the Isle of Patmos because of his testimony (Rev 1:9).
3 “our” is not present in the Greek text, but was supplied to bring out the sense in English.
4 Grk “dear.” The adjective is functioning as a substantive; i.e., “dear one” or “dear friend.”

In other versions

Paul, a prisoner for Christ Jesus, and Timothy our brother,

To Philemon our beloved fellow worker

Paul, a prisoner of Christ Jesus, and Timothy our brother,

To Philemon our dear friend and fellow worker—

Paul, a prisoner of Christ Jesus, and Timothy our brother:

To Philemon our dear friend and coworker,

This letter is from Paul, a prisoner for preaching the Good News about Christ Jesus, and from our brother Timothy.

I am writing to Philemon, our beloved co-worker,

Paul, a prisoner of Christ Jesus, and Timothy our brother, to Philemon, our dear friend and fellow worker,

Paul, a prisoner of Jesus Christ, and Timothy our brother, unto Philemon our dearly beloved, and fellowlabourer,

Public Domain