Combine potatoes, shallot, horseradish, mustard, garlic salt and pepper in a medium bowl. Spread each portion of fish with 1 teaspoon mayonnaise, then top with one-fourth of the potato mixture, pressing the mixture onto the fish.
Heat oil in a large nonstick skillet over medium-high heat. Carefully place the fish in the pan potato-side down and cook until crispy and browned, 4 to 5 minutes. Gently turn the fish over, reduce the heat to medium and continue cooking until the fish flakes easily with a fork, 4 to 5 minutes more. Serve with lemon wedges.