Which is the correct spelling fairy or faerie?

According to bit difference, Nevertheless, there is currently a difference in meaning that can be drawn between the two spellings when used in certain settings! Specifically, fairy tales and the concept of fairies that goes along with them often relate to the type of folk stories recorded by the Brothers Grimm.

Fairy has a lot of alternative spelling : faerie, fae, fay, fey, fair folks, the list goes on

This stemmed from a cultural belief that you shouldn't invoke their name (as in, "say A's name and A will appear"), because that might invite them to your home.

English mostly use fairy (singular) and fairies (plural).

Some people might use faerie for aesthetic reasons