Turn on the oven to preheat to 225 degrees. Grease a baking sheet with vegetable oil and place in the oven in the middle position.
In a bowl, combine mayonnaise, brine, capers, hot sauce, and 1/8 teaspoon of salt. Set aside.
In a shallow bowl, combine wheat flour, paprika, 1/4 teaspoon of garlic powder, 1/8 teaspoon of salt, and black pepper.
Pour the whipped egg whites into another shallow bowl.
In a third bowl, mix together the cornmeal, 1/8 teaspoon salt, and 1/4 teaspoon garlic powder.
Take fillets one at a time, first coat in wheat flour on all sides, then in proteins, and finally in corn flour.
Put the breaded fillets on a heated oiled baking sheet, lightly sprinkle the fillets with vegetable oil, and place in a preheated oven for 6-8 minutes.
Turn the fillets over, sprinkle with vegetable oil and cook for another 6 minutes.
Cut the buns in half. On each of 4 serving plates, place one half-base bun, on which 1/4 cup lettuce leaves, 1 fillet, 1 slice of onion, and 2 slices of tomato.
Grease each half-top of the bun with 4 teaspoons of mayonnaise sauce. Cover the burgers with these tops and serve immediately.