Both forms are correct. Wether and whether are both correct, but there are some significant differences between these at glance very similar words. At the forefront, we see two words with identical pronunciation and almost identical spelling. When it comes to meaning, wether is a noun describing a particular kind of sheep. While whether is a conjunction used to report questions or doubts. On the surface, these words are very similar, but definitely should not be mistaken.

Correct spelling, explanation: noun naming a specific kind of sheep.

Correct spelling, explanation: common conjunction used to express doubt or possibilities.

Definition of wether:
noun: a male sheep, which has been castrated;
My grandfather was a grazier, he had a big farm with hundreds of sheep and he specialized in wethers.

Definition of whether:
conjunction: if;
I am questioning whether we have enough money to buy a house.
I doubt whether our school can handle another budget cuts.
– also a phrase whether…or, used to express that it is not important if;
I will fail this exam, whether I learn more or not.
Someone has to clean this mess, whether it is you or me.