Why did they exterminate Jew for crucifying Jesus

They were exterminated because Pontius Pilot (the guy in charge of law in 1st century AD) offered the Jews an option of who to save Barbas or Jesus Christ and the Jews chose Barbas to be saved and Jesus to be condemned. Pontius Pilot did this because it was Passover and he did this out of respect to the Jewish tradition, not to kill anyone on the Jewish holiday. Therefore, the Jews are blamed for the crucifixion of Jesus Christ, though many argue that they were swayed into choosing Barbas to be saved rather than Jesus.