Mix the cornmeal, flour, salt, paprika, and pepper together in a shallow dish or plastic container. Pour the milk into another dish. Dip the fillets into the milk, then into the cornmeal mixture, coating them well and shaking off any excess.
Heat 1/2 the butter in a large skillet over high heat, and fry 2 of the fillets for about 3 minutes on each side, or until the fish flakes easily when tested with a fork. Transfer the fillets to a serving platter and keep warm. Repeat with the remaining butter and fillets. Serve immediately, with tartar sauce and lemon wedges.