Pat the fish fillets dry with paper towels, then season lightly with salt and pepper on both sides. Set up a breading station with three shallow dishes: one with flour, one with beaten eggs, and one with panko breadcrumbs mixed with paprika and a pinch of salt and pepper.
Dredge each fillet in the flour, shaking off excess, then dip into the beaten eggs, ensuring complete coating. Finally, press the fillet into the panko mixture, turning to coat evenly, and set aside.
Heat a shallow layer of oil in a skillet over medium heat until shimmering and hot but not smoking. Carefully place the breaded fillets into the pan, without crowding, and cook for about 3-4 minutes per side, until each side is golden brown and the fish flakes easily with a fork.
Remove the cooked fillets from the pan and place on a paper towel-lined plate to drain excess oil. Toast the burger buns lightly if desired.
Assemble the sandwich by placing a lettuce leaf on the bottom bun, followed by the crispy fish fillet, tomato slices, and a dollop of tartar sauce. Cover with the top bun and serve immediately.
Serve the Filet-O-Fish sandwich hot, with optional sides like chips or a salad for a complete meal.