Jesus didnt say he was a jew. He is the Christ, the Father.
Pilate asked if He was king of the Jews (and people ran with it). Jesus replied, "Thats what you say".
Pilate hung that on the cross.
Jesus didnt answer him that He was or wasnt, because Jesus Christ was King of ALL, meaning mankind, beasts, sea, sky air rocks.....
Later, He said He was COME BUT TO THE HOUSE OF ISRAEL.
JEW AND ISRAELITE ARE NOT INTERCHANGEABLE TERMS.
The Southern Empire, after the split, was composed of the Tribes of Judah and Benjamin. THEY CALLED THEMSELVES JEWS.
The Northern Empire was callec the ISRAELITES, though modern religion ignores these facts as desdribed in the BIBLE. The Israelites did not call themselves Jews.