Sorry, just to be clear, are you asking whether Jesus was a kohen, i.e. a Jewish priest?

No, indeed. The traditional descriptions of the genealogy of the man (of which there are two, which differ, but not in this respect) concur that he is of the Tribe of Judah and of the Davidic line. And this is a natural and necessary function of the traditional treatment of the Messianic prophecy, as foretelling such a Davidic Messiah.