Fill a deep, heavy-bottomed skillet with about 2½ inches of oil. Heat over medium until oil registers 365ºF on a deep-­fry thermometer. Meanwhile, whisk together cornmeal, red pepper flakes, and cayenne in a shallow dish; season with salt and pepper.

Rinse catfish and pat dry with paper towels. Season with salt and pepper. Dredge fillets in cornmeal mixture, turning to coat both sides. Working in batches, carefully submerge fillets in oil and fry until crust is crisp and golden and fish is cooked through, about 3 minutes. With a slotted spatula, transfer to a large plate. To serve, spread bread slices with mayonnaise and/or relish, as desired. Layer with catfish and onion slices.
Serve immediately.