the question was about “Flavius Josephus” – please excuse typos.
As I noted meanwhile he’s [allegedly] also known as “Joseph ben Mathitjahu ha Kohen”
don’t know if _that_ is true.
But I suppose he was a jew – correct me if I am wrong.
A good week,
In Jewish writings he is known as you wrote. I am not a historian, but this is the way it seems.