On a large piece of wax paper, mix together paprika, cayenne pepper, black pepper, onion powder, thyme, basil, garlic powder, and oregano.
In a small saucepan, over medium heat, melt butter or margarine with oil. Brush both sides of the snapper filets with the butter mixture, reserve the remaining butter mixture. Coat both sides of the filets with the seasoning-mixture.
Heat a large cast-iron skillet over high heat until a drop of water sizzles on it. Drizzle half of the remaining butter-oil mixture on one side of fish fillets. Place fillets butter side down in pan. Cook over a high heat until the fish is deeply browned, about 5 minutes. Drizzle remaining butter-mixture over the fish and flip the fish over. Cook until fish is browned and flakes when tested with a fork, about 5 minutes more. Season to taste with salt.