“Satan” means “adversary.”
[TODO etymology and history]
Jesus denounced his fellow Jews by calling them descendants of an unnamed evil god.
[TODO quote here]
Competing religions existed in the area later known as Judea long before Judaism existed.
[TODO link to argument that Judaism started in 440 BC.]
The competing priesthoods of Jah and Elohim probably denounced each other as followers of evil gods long before Judaism was invented.
Thus to a priest of Jah, Elohim was an “adversary” or a “Satan,” (or a group of Satans) and to a priest of Elohim, Jah was an adversary.
So it is entirely possible that the people whose descendants eventually became known as Jews had been calling each other “children of Satan” long before there was any kind of Jewish identity.