From the end of the Second Jewish Revolt and the Diaspora, around 130 AD, the Jews lived more or less quietly in the Roman Empire. They settled in cities all around the Roman and the Parthian Empires. Many Jews also moved to the trading cities of the Arabian peninsula. Probably because of the Diaspora, many Jews now gave up farming and became traders. Jewish families arranged to have brothers and sisters or cousins in different cities. That way they had trading partners they could trust. Many Jews learned Latin and Greek, and some Jews gave up speaking Aramaic or Hebrew.
But a lot of people in the Roman Empire converted to Christianity in the 300s AD. That brought new problems to the Jews. The Roman emperors Constantine, Constantius, and Theodosius encouraged or forced everyone to become Christians. Sometimes they tried to convert the Jews along with everybody else. Many Christians believed that if there was anyone near them who was not a good Christian, their own immortal souls were in danger of going to hell. So they had a duty to convert everybody. If they failed, they might go to hell.
But not everybody thought the Jews should become Christians. Some Christians believed that the Jews were special to God and should be left alone, as long as they kept to themselves and didn’t try to interfere with Christians. So the Jews were sometimes treated very badly, and other times less badly.