Aelian, a natural philosopher in the 3rd century AD, gives a wonderfully naturalistic description of the Griffin in his encyclopedia of animals, De Natura Animalium:
‘Men commonly report that it is winged and that the feathers along its back are black, and those on its front are red, while the actual wings are neither but are white. And Ctesias records that its neck is variegated with feathers of a dark blue; that it has a beak like an eagle’s, and a head too, just as artists portray it in pictures and sculpture. Its eyes, he says, are like fire. It builds its lair among the mountains, and although it is not possible to capture a full-grown animal, they do take the young ones.‘ [ref] Aelian, On the Characteristics of Animals, translated A. F. Scholfield Loeb Classical Library [/ref]
Close to a millennium later, Adrienne Mayor in her book, The First Fossil Hunters [ref] Adrienne Mayor, The First Fossil Hunters: Paleontology in Greek and Roman Times (Princeton University Press 2000) revised 2011 with new introduction. [/ref] presents an intriguing theory that it was actually people coming across the fossilized bones of protoceratops in the mountains of central Asia, that gave rise to the myths of the griffin. Protoceratops was a relative of the more famous triceratops, though it didn’t have horns and would only grow to the size of a large sheep [ref] https://museumsvictoria.com.au/website/melbournemuseum/discoverycentre/dinosaur-walk/Meet-The-Skeletons/Protoceratops/index.html [/ref]. If you look at the skeleton of the Protoceratops, you can certainly see many Griffin like features.
Protoceratops andrewsi in Cosmocaixa, Barcelona. Photo by Eduard Solà. Distributed under Creative Commons Attribution-Share Alike 3.0 Unported license
Fossilized clutches of dinosaur eggs may also have been discovered among the bones, further supporting the avian nature of the Griffin. Another aspect of the Griffin mythology was that it was always guarding gold, and the area where the Protoceratops fossils were found was indeed an area where ancient miners would sift the soil for flakes of gold. It is not hard to imagine, that a person out in the desert coming across the strange bones might see them as proof that Griffins inhabited the area.
However, others have said that the creation of the griffin was simply a combination of two existing creatures, the lion and the eagle, and similar monstrous combinations of great cat and bird of prey occurred in the mythology of other cultures that predated the stories travelers brought to the Greek writers [ref] http://markwitton-com.blogspot.com.au/2016/04/why-protoceratops-almost-certainly.html [/ref].
There are certainly plenty of other examples of hybrids in the monster world that don’t correspond to any fossil record. The cockatrice was a mix between a rooster, bat and snake; the hippocampus, was a marine creature with the upper body of a horse and the lower body of a fish; and that is not to mention any number of human animal hybrids, such as harpies, centaurs and the sphinx.
That is not to say though, that Mayor’s theory is incorrect, or that even if the discovery of the Protoceratops came after, it may have been seen as proof to reinforce the existence of Griffins. The strange Protoceratops bones exposed in the rock, might certainly have been enough to have a miner far away from home nervously watching the mountains above in case a Griffin decided to swoop down.
a hatchling ceratopsian dinosaur, Protoceratops andrewsi, at the American Museum of Natural History in New York. Distributed under Creative Commons ShareAlike 1.0 License
This may have been one of those young griffins that Aelian says could be captured.