Answer:
Yes he did
Jesus was a Jew, born into a Jewish family through a Jewish mother. He prayed at the Temple and in synagogues. He was (and is) the Saviour of the world, but He was the Jewish Messiah and His identity is confirmed because He fulfilled the Jewish Messianic prophecies.
He was also the Son of God and God the Son, the second Person of the Holy Trinity that He revealed as intrinsic to the character of God.
Of course, this was His mission: to bring forth out of the Old covenant the fulfillment for which it prepared us. The Jews were (and are) the first people to whom God Personally spoke, with Whom He made a Covenant. It was this Covenant, which promised the Messiah, that paved the way for the New Covenant that was the product of His arrival.
At the last, He died the Sacrificial victim offered up by the Temple Priesthood, thus fulfilling all righteousness. Then He arose, and it was all made new.
Of course, Jesus was a Jew. He was born of a Jewish mother, in Galilee, a Jewish part of the world. All of his friends, associates, colleagues, disciples, all of them were Jews. He regularly worshiped in Jewish communal worship, what we call synagogues. He preached from Jewish text, from the Bible. He lived, was born, lived, died, taught as a Jew. But, of course, it does need to be said because we all know what happens later in the story, where it turns out that Christianity becomes something other than Judaism and as a result, Jesus in retrospect is seen not as a Jew, but as something else, as a founder of Christianity. But, of course, he was a Jew.
