Jeremy is one of Prince Adam's younger cousins. His exact relationship to the Eternian royal family is unclear, though he is presumably the son of one of King Randor's siblings, and thus the grandson of King Miro. Jeremy's only appearance is "The Royal Cousin"; his royal title, if he has one, is never stated in the episode.
Jeremy was only a baby when Adam first saw him, and the two did not meet again until about a decade later. At that time Jeremy was a sullen, obnoxious brat. However, his misadventure with Evil-Lyn and the rock softener taught him a lesson in humility.