Dialectal or archaic variant of 'faun' (a mythological creature) or a local/regional term of uncertain meaning.
Possibly a dialectal spelling variant of 'faun' from Latin 'faunus' (Roman god of the forest), though the exact origin and meaning are obscure. It may also be a completely separate regional term.
Words like 'fany' show how dialect and spelling varied wildly before standardization—the same creature might be written as 'faun,' 'fany,' or 'fayne' depending on where and when you lived.
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