There are a few different kinds of them.
Harpie
Sirens
Bird-People
a half woman and a half bird in the Odyssey is called a Siren.
Half human-half dog is called a youkai. half human-half fox is called kitsune
No bird can be described as half bird/half mammal. The Duck Billed Platypus was thought to be a "mixture" of animal types when it was first discovered, but the "bill" is unlike a true bird's bill.
A half fairy and half human is typically referred to as a "half-faerie" or "half-fey".
Fae.
Nephilim
Are you sure you're not talking about a flying squirrel? They don't fly, but they glide. I don't think there is such thing as a half bird, half squirrel. If there is, combine bird and squirrel. (Squird or Birrel or something)
There is no fantasy creature that is half horse half human and NOT called a centaur.
What about a Hippogriff? It is an imaginary animal with a horse's body and a hunting bird's wings and head. Or, a centaur, which is half horse, half human? Or a faun (half goat, half human)?
No, it is not possible Not possible in this world. Humans and dogs have different number of chromosomes and can't interbreed. In reality no, our chromosomes are too different to be able to produce offspring.
A Sphinx
it is a centaurs