Combine the mashed potatoes, egg, onion, salt, and pepper in a bowl. Mix until blended (do not overmix). Heat the oil in a non-stick frying pan over medium heat. When hot, add about 1/4 cup of the potato mixture to the frying pan in a patty shape. Flatten to about 1/2-inch thick. Let the patty cook until the bottom is brown and crispy. Turn the patty over with a spatula and let the other side cook until brown and crispy. Remove to a paper towel to drain. Repeat with remaining potato mixture. Serve the patties hot with ketchup or sour cream.