Add oil to a heavy skillet, such as cast iron, until it reaches about halfway up the sides.
Heat the oil to 350 F. A good test to check the oil temperature is to flick a little of the dry breading mixture into it. If it sizzles, the oil is ready.
Dredge catfish fillets in the flour mixture, shaking gently to remove excess. Lay a couple of fillets gently in the hot oil and fry for 2-4 minutes, depending on the thickness of the fillets. Turn fillets with a spatula and cook for another 2-4 minutes or until golden brown.
Remove and keep warm in the oven on low while frying the remaining fillets.