Both forms are correct. Whether and wether are two correct forms. Both words are homophones, which means they sound the same and, what is more, in spelling, they differ by only one letter. Having so much in common superficially, it may be surprising how different they are in meaning. Whether is common conjunction used to express doubt or possibilities. Meanwhile, wether is a noun naming a specific kind of sheep. As we can see, it is good to avoid confusing these two words.

Correct spelling, explanation: conjunction used to report questions or doubts.

Correct spelling, explanation: a noun describing a particular kind of sheep.

Definition of whether:
conjunction: if;
She wasn’t sure whether he’d like her new appearance.
I am wondering whether I want dessert.
– we can use it as a phrase whether…or, meaning that something is not important if;
I’m cutting my hair, whether she likes it or not.
It doesn’t matter now whether you take a train or a taxi to the airport, you’re going to miss your plane anyway.

Definition of wether:
noun: a castrated male sheep;
His farm is well-known for breeding premium quality sheep, especially wethers.