From Bulbapedia, the community-driven Pokémon encyclopedia.
The Old Amber is a fossil from the Generation I games and their Generation III remakes.
It can be obtained in a back room of the Pewter Museum of Science. The HM for Cut is needed to get there, as a bush blocks it off. It is given to the main character by one of the scientists working there. If brought to the laboratory on Cinnabar Island, the Old Amber can be regenerated into an Aerodactyl.
The Old Amber is different than the other fossils, being a type of fossilized substance rather than a fossil named by its appearance. It is possibly inspired by Jurassic Park, in which genetic engineers extracted DNA from mosquitos trapped in amber and used it to recreate dinosaurs.