Petey can be found inside of the Common Room within Fossil Stadium. If the player shows him a Spinax, Venator, and Megalo he'll challenge them to a Fossil Battle. He would seem fairly easy, but he does have Rank 3 and Rank 4 Vivosaurs, but he is the first opponent you face (depending on the time in which you battle him) to use Vivosaurs with the Link Ability. If you win with those three Vivosaurs he will reward you a red boned fossil rock of a Metria part (not the head, you have to find that on your own). If you manage to break it you can't get another one. Eventually you gain the ability to fight them again. But you need Jiango, Stego, and Kentro. His team in this second match consists of a Rank 8 Salto, Rank 7 O-Raptor, and Rank 7 Ankylo. If you win with them, you'll acquire another red boned fossil.
"Now that I have these awesome vivosaurs... I would kill for a chance to battle against Stego, Jiango and Kentro, my new favorites."
(with correct team)
"All right! You brought Stego, Jiango, and Kentro! Yippeee! OK, let's battle!"
(If you decline)
"B-but... How could you do that to me? I'm only little!"
(If you accept)
"I'm gonna give you a workout this time!"