[Simplemen]

Yes, they are conquered by a lot of countries but Rome did allow Judaism as legal religion at several point of history. When Caliphate conquered Jerusalem, they start converting these Jews because Islam has high focus on memberships. Mind you, my Muslim friends too agree membership is a big deal in Islam. So naturally, when you try to convert people, you are doing a minimum death ethnic cleansing.

Since Jews originated from Jerusalem, naturally they run to surrounding regions like Europe, North Africa, Middle East.

So you listen to your friends rather than find out from legit sources? 

You contradicted yourself when you said they ran to seek refuge & settled in Muslim lands for hundreds of years, and in the same breadth they were ethnically cleansed by the Muslims.