I save this cooking for outside because of the smoke. You need lots of very hot oil, with very cold fish and batter. I put my fish and batter in bowls surrounded by ice to keep them chilled and get the oil hot with a gas burner. Hot oil and cold fish is the key to a crispy coating with less oil saturation. Fatty fish is usually not deep fried but some people do enjoy them saut ed in a frying pan.
Fatty fish is considered to be best when broiled, baked, or put on the charcoal grill.
One thing about fish is that you never want to over cook it because no matter how fresh a fish is, if you overcook it and it starts to burn, it will stink like old rotten fish.