Its unlikely that any of us are 'part' fae or fairy.
There are elemental earth energies we tend to call fairy or fae, they do not exist in the 3rd dimensional earth though, more like the 4th or 5th dimension.
It's unikely there's cross deminsional breeding, but I could be wrong. If you meet some one who seems to be rather see-through and not fully formed into physicallity and claims to be a fairy half-breed then let me know! I'd love to be wrong about this :)