Pour buttermilk into a shallow bowl.
Add the flounder fillets, ensuring each piece is fully submerged.
Refrigerate for about one hour to allow the flavors to meld.
In another shallow dish, mix the flour, cornmeal, salt, black pepper, and paprika.
Make sure the mixture is well combined for an even coating.
Remove the flounder from the buttermilk, allowing any excess to drip off.
Coat the fillets in the cornmeal mixture, pressing gently to ensure the coating adheres.
Heat oil in a heavy skillet over medium-high heat.
The oil should be about 1/8 inch deep and shimmering when ready.
Place the coated flounder in the skillet.
Brown on one side for 2 to 3 minutes.
Turn carefully and cook an additional 3 minutes or until the fish flakes easily with a fork.