Preheat the oven to 425 degrees Fahrenheit. Place a wire rack onto a rimmed baking sheet and set aside.
Pour the panko breadcrumbs into a large skillet and toast over medium-high heat, stirring constantly. Cook until the breadcrumbs are a light golden brown, then pour them into a large, shallow dish (pie plates work great). Set aside and allow the breadcrumbs to cool fully.
Pour the ⅓ cup flour into a second shallow dish and set aside.
Whisk together the eggs, remaining 2 tablespoons of flour, paprika, cayenne pepper, horseradish, and mayonnaise in a medium-sized bowl until no lumps remain. Season with salt and pepper, then set aside.
Dredge the cod filets by gently dipping the filets in the flour, making sure both sides are evenly coated. Shake off the excess flour, then dip the filets into the egg mixture. Finally, dip the filets into the breadcrumbs and place them onto the wire rack.
Bake the filets in the preheated oven for 15 to 20 minutes, or until the fish is fully cooked and flaky. Serve the fish immediately.