Puree the cranberry sauce with the nutmeg and lemon zest in a food processor. Reserve.
In a large bowl, whisk together the mashed potatoes, milk, 1/2 cup sugar, melted butter, vanilla, cinnamon and eggs until smooth. Add the flour, baking powder and salt and stir with a rubber spatula until just combined. Cover with plastic wrap and refrigerate for 1 hour.
Heat 2 inches of oil in a heavy-bottomed pan until it reaches 350 degrees F. Place the remaining 1/2 cup sugar in a shallow bowl.
With a 1-tablespoon scoop, carefully drop the batter into the hot oil; work in batches to avoid crowding the pan. Fry until deep golden brown and cooked through, about 2 minutes per side, turning with a slotted spoon. Remove to a paper towel-lined plate to drain for a few seconds, then roll in the sugar.
Serve with the cranberry dipping sauce.