Yes you can use a Turkey fryer to fry fish with and it will work just fine.
A Turkey Fryer can be used to fry any foods that you want to fry with it but it's just made large enough to fry Turkey in.
Also do not put frozen fish or frozen turkey or any other frozen meat or foods into a hot Turkey fryer as it can cause a flash fire and burn yourself badly and lead to severe injury or even possible death and can burn your house down.
I use my Turkey Fryer for Frying Turkey on Thanksgiving and Christmas but I also use it to fry fish as well as chicken and anything else I can think of to fry in it.