Put the catfish a shallow pan and cover with water. Add a tablespoon of the salt, cover with plastic wrap and soak overnight in the refrigerator.
Mix the cornmeal, flour, the remaining1 teaspoon salt and the black pepper in a plastic bag. Drain the water from the catfish and transfer the fillets one at a time to the bag with the cornmeal. Shake the bag to coat the fish and place on a sheet tray or platter.
Heat the oil in a deep fryer or Dutch oven to 300 degrees F.
Drop a few fillets into the hot oil. Do not overcrowd. Cook the fish until golden brown, about 10 minutes. Remove the pieces with a slotted spoon and keep warm in an oven while frying the remaining pieces.
Recipe adapted from Home Cooking with Trisha Yearwood (c) Clarkson Potter 2010