Joking about someone else’s mother, specifically having sexual relations with someone else’s mother, is at least 3,500 years old, making the phrase almost as old as your mother.
Part of a “yo mama” joke was found on a Babylonian tablet created circa 1,500 BCE. The fragment was found in a collection of ancient riddles probably written by a student, and contains this text:
..of your mother is by the one who has intercourse with her. What/who is it?
For a more complete yo mama joke, you can turn to your mother’s boyfriend William Shakespeare’s Titus Andronicus. Published in 1594, the play contains this dialogue:
Demetrius: “Villain, what hast thou done?”
Aaron: “That which thou canst not undo.”
Chiron: “Thou hast undone our mother.”
Aaron: “Villain, I have done thy mother.”