What is Babylon's ethnicity ?

Mesopotamian.

Mesopotamia used to be where today is Iraq. Babylon was a city in Mesopotamia.

Due to the wandering of people, it is hard to tell what contemporary ethnicity would be closest to the Mesopotamians. The Babylonian Religion is extinct, though some of their Gods have found their way into modern religions. (The Babylonian god Baal for example has been referred to as a Demon by other peoples. So the Beelzebub is basically a successor of that Babylonian god.) Babylonian customs and traditions are also out of use.

The question makes no sense. What is Russia’s ethnicity? What is Rome’s ethnicity? A place has no ethnicity.

I would like to make one correction if I could Mesopotamia was a nation in the olden times therefore Mesopotamian would be a nationality not an ethnicity. An ethnic group (or ethnicity) is a group of people whose members identify with each other, through a common heritage, often consisting of a common language, a common culture (often including a shared religion) and an ideology that stresses common ancestry or endogamy. Therefore the ethnicity of Babylon would be Middle Eastern.