Why did the Jews leave their lands in the north of the Arabian Peninsula and come to Medina?

The Jews came to Medina, fleeing persecution by Christians in Al-Sham (Greater Syria), due to what the Jews believed about Jesus and his mother (peace be upon them both). It was also said that a group of them came to the Arabian Peninsula and settled around Yathrib after they fell short in fighting the Amalekites and disobeyed the command of Moses (peace be upon him), so their people refused to allow them back into their lands.