I assume Atari Track Ball.
Natively the Atari trackball does not work as an Amiga mouse. But there was an article on how to modify it to work as one. I did it once. Unfortunately that trackball fell when packing for a show and I don't have it anymore. I think they called it the Atari (or Amiga) trackmouse. That might make looking for the instructions easier. Would likely have been an issue of Amazing Computing.
