Correct spelling, explanation: this is the correct form, because of the root word enemy (with the suffix -ity added). It was spelled similarly also in its Middle English origin enemite (e was probably skipped later due to pronunciation). Emnity is a mistaken form, probably caused by often sound mn (as in gymnastics, firm). The only correct form, though, is enmity.

Definition of enmity:
noun, a state of hostility
His enmity towards us was obvious.
There was much enmity between the Capulets and the Montagues.

Incorrect spelling, explanation: emnity is a mistaken spelling, probably caused by popular sound mn (like in words column or solemn). This word however should be spelled enmity, because of its roots enemy (emenite in Middle English). Therefore enmity is the correct form.