Was it Paul or Peter or someone else?
Is this contemporary contention a heresy?
I need to know the thrust of the discussion please thanks
We know it wasn't one of the original apostles because the author says this: Hebrew 2:1, “[The message] was declared first by the Master, and it was attested to us by those who heard.”
This means he was probably a disciple of one of the original twelve, or possibly of Paul. He seems to write with some authority, as one transmitting an apostolic tradition (cf. Heb 5:7)
The early church thought it was Paul, but there are some things that mitigate against this. First, the Greek is excellent, unlike Paul's. Second, the theology is not particularly Pauline. Third, this epistle is written to Jewish believers and Paul's mission was to Gentiles.
There are clues though that indicate it may have been written by someone in Paul's entourage. For instance, the epistle references Timothy's release from prison and the author's anticipation of his arrival.
Clement of Alexandria cites traditions for Luke and Clement of Rome as authors. (Eusebius,
Ecclesiastical History, 3.38.2)
I think Clement of Rome fits the bill, as does Eusebius:
Others claim that it was Clement himself. This seems more probable because the epistle of Clement and that to the Hebrews have a similar character in regard to style, and still further because the thoughts contained in the two works are not very different. (Eusebius, Ecclesiastical History 3.38:2–3)
Modern scholars reject Clement, mostly on theological grounds because Clement held a high view of Temple and its services as a model for the Christian church.