Persian Empire period
Under the Parthian, and later, Sassanid Persians, Babylon (like Assyria) remained a province of the Persian Empire for nine centuries, until after 650 AD. It continued to have its own culture and people, who spoke varieties of Aramaic, and who continued to refer to their homeland as Babylon. Some examples of their cultural products are often found in the Babylonian Talmud, the Gnostic Mandaean religion, Eastern Rite Christianity and the religion of the prophet Mani. Christianity came to Mesopotamia in the 1st and 2nd centuries AD, and Babylon was the seat of a Bishop of the Church of the East until well after the Arab/Islamic conquest.
How interesting! Thank you Elsie. That most certainly deserves more study.