Combine the sugar, mashed potatoes, milk, eggs, nutmeg, baking powder and flour in a large bowl in the order listed, mixing well after each addition.
Roll 1/3 of the dough to 1/3 inch thickness on a lightly floured surface.
Cut with a floured doughnut cutter.
Repeat with remaining dough.
Have all doughnuts ready before frying, for they cook very fast.
Fry in deep vegetable oil at 375 degrees until brown on both sides, turning once.
Drain on paper towels.