When I put leftover mashed potatoes in the fridge, I put them in s container that is small enough to invert and slice for 1/2 inch patties. The potatoes do have to be firm before you put them up, however. I keep instant potatoes on hand to mix in just for this reason.. After slicing up the patties, I just dip them in seasoned flour, then in an egg wash then back in the flour again and fry in 1/4 inch shortening till brown on both sides. Have been diong this for 40 years, and it still works!