Yes. “Fey” is the correct spelling. They use it because while they are fae, and also fay, they are in fact fey, so they are constantly starving to death.
Their world name is the Silver Dawning. Being among the Mythos, they are naturally magical beings, producing their own magic like an electric eel generates shock – but unlike every other member of the Mythos, their magic is being stolen from them.
The Throne and the Scepter siphon their power, leaving anyone claimed by those two artefacts of power starving. They’ve found ways around it. They can weave magic from human love and other emotions as well as other people’s magical arcanum.
The primary group among the Fey are the Seelie and Unseelie, who resemble humans, though they have long, pointed ears. Males are called feyor. Females are called feyan.
As Fey age, they their skin and flesh lose their softness. In the end, when Fey are about to die (if they lived to old age, that is), they resemble statues.
Trivia: Dragons call them children of the grasses because they scuttle around in the grass (from a dragon’s point of view).