Pegasus
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It's a horse with wings. You like horses? You like flying? Yeah, a pegasus has you covered on both accounts.
Originally "Pegasus" was the name of a specific horse, Medusa's rape-child after Poseidon plowed her. His wings were attached to his shoulders, to make it easier for his human riders to actually ride him. Since then the word has become a common noun to refer to any horse with wings, and nowadays the wings are further back, towards the bottom of the ribcage. Requires magic to work as horses have the aerodynamics of a brick.
Beware of horse apples falling from high altitude.
Warhammer Fantasy
In the wild and weird world of WHFB, Pegasi are natural creatures with connections to the winds of magic, while they look like horses from the outside, on the inside they are completely different, sharing anatomical structures with birds and possessing hollow bones. Despite this, and owing to their innate magical nature, they are fully capable of carrying a heavily armored warrior on their back and flying for over 12 HOURS without visible strain. Also, they are omnivores, feeding on carrion as well as vegetation. The more tainted ones are of course fully carnivorous possessing horrifying mutations ranging from mouths of full of rending fangs to wings akin to that of bloodthirsters. Bretonnian, and Imperial knights and nobles alike seek out pegasi for both their majesty and their status as the steeds of powerful people. Balthasar Gelt has his pegasus Quicksilver who he likes to uparmor with his lore of metal.
Monstergirls
Pegasi monstergirls are rare because the standard approach to doing them, making them into a winged centaur, looks rather overly complicated in the eyes of many.