In a medium bowl mix potatoes, eggs, onions, and cheese. With about 1/2 cup of mixture form potatoes into individual patties. Heat skillet and melt some butter or margarine in it. Fry patties until outside is crispy and inside is hot. Serve with sausage links or other simple main dish.
OPTIONAL: You can top patties with sour cream or left over gravy.
MAKE THIS A MEAL BY TOPPING PATTIES WITH A MEAT AND GRAVY MIXTURE. Mom might use left over turkey or chicken and gravy, for example.