Pat the fish fillets dry with paper towels, then cut each into the desired size for a sandwich. Slice tomatoes and wash lettuce if using fresh toppings.
Set up a breading station with three shallow dishes: one with flour, one with beaten eggs, and one with panko breadcrumbs mixed with paprika, salt, and black pepper.
Dredge each fish fillet in flour, ensuring even coating. Shake off excess flour, then dip into the beaten eggs, and finally press into the panko mixture until fully coated, creating a crispy crust.
Heat vegetable oil in a frying pan over medium heat until shimmering and at least 350°F (177°C). Gently place the breaded fillets into the hot oil, avoiding overcrowding, and fry for about 3-4 minutes per side, or until golden brown and cooked through. Use a thermometer to confirm internal temperature of 145°F (63°C).
Remove the cooked fish fillets from the oil and drain on paper towels. Toast the burger buns lightly if desired. Assemble the sandwich by placing the fried fillet on the bun bottom, adding desired toppings like lettuce and tomato, then spreading tartar sauce if using. Cover with the top bun to serve.
2 fillets white fish fillets (cod or haddock)