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Yes Jesus was Jewish:
John 4:9 Then the woman of Samaria said to Him, "How is it that You, being a Jew, ask a drink from me, a Samaritan woman?" For Jews have no dealings with Samaritans.
John 18:35 Pilate answered, "Am I a Jew? Your own nation [i.e. the Jews] and the chief priests have delivered You to me. What have You done?"
I hope you have found this helpful.
God bless you,