In a large bowl mix together flaked fish, mashed potatoes, onion, 1/4 cup flour, eggs and parsley. Season to taste with salt and pepper. Form the mixture into 12 small patties.
Place the remaining 1/2 cup flour in a shallow dish and season with salt and pepper. Stir to mix well.
Heat about a 1/4-inch of vegetable oil in a heavy-bottomed skillet over moderately high heat. Dredge the fish patties in the seasoned flour, shaking off any excess and add them to the hot oil. Cook untill browned on both sides; about 8 minutes total, turning once. As the patties are cooked, transfer them to paper towels to drain. Serve hot.