To keep the first batch of fried fish hot while frying the rest, place fish on a heatproof serving platter. Keep warm in a 250°F oven until ready to serve.
Place fish fillet, skin side down, on cutting board. Run fingertips along surface of fillet to feel for bones. Remove any bones with needle-nose pliers or fingers.
Starting at tail end or shortest side of fillet, work the edge of a boning or carving knife between the flesh and skin to separate the flesh from the skin. Grasp end of skin with paper towel and pull on it as you run knife in opposite direction down length of fillet. Keep knife angled down slightly as close to skin as possible, using a gentle sawing motion if necessary. Remove skin; discard.