Pour the oil in a large skillet to a depth of 1/2 inch and place it over medium-high heat until it registers 350°F (177°C) on a deep-fry or candy or instant-read thermometer. You want the oil to be hot but not smoking. Set out a wire rack over a baking sheet or place a brown paper bag on the counter.
Place the cornmeal in a medium bowl and stir in the salt and pepper. Dredge the fillets in the cornmeal mixture to coat on both sides.
Reduce the heat to medium. Place the fillets in the skillet and cook, turning once, until browned on both sides, 3 or more minutes per side, depending on the size of the fillets. (Be careful not to crowd the fillets. You may need to work in batches.) Transfer the fillets to the wire rack or brown paper bag.
Serve the fish hot with the lemon wedges, vinegar or hot sauce, and/or tartar sauce.