Rinse the fillets. Cut into three to four strips lengthwise, at a slight diagonal. Season fish with salt, pepper, and Old Bay, rubbing into fish; set aside. Preheat fryer to 375 degrees F or heat enough oil to fully submerge fish in a large, deep-sided, iron skillet. 

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Whisk the cornmeal, flour, and BBQ rub together in a large bowl. Dredge catfish fillets in the mixture until well-coated, shake off excess, and set aside. Once the oil is heated, pass fillets through the cornmeal mixtures again, shake off, and carefully slide fish into the fryer with the basket lowered. Fry only a few at a time so as not to overcrowd and bring down the temperature of the oil. 

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Fry until fish floats and is golden brown, about 4 to 6 minutes. Drain on several layers of paper towels or brown paper bags before transferring to a platter or individual plates. For hushpuppies, add enough buttermilk or milk to the remaining dredging cornmeal to form a thick batter and drop by spoonfuls into the hot oil until browned and cooked through. Offer hot sauce or tartar sauce at the table. 

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Tip: Frozen catfish sometimes has a muddy flavor to it. Remove any fat and/or dark flash that is present on the fillets and soak them for 30 minutes at room temperature in salt water, with 1 tablespoon of salt for a quart of water. You may also cover them with buttermilk.