Heat the oil. Attach a deep-fry thermometer to a deep, heavy saucepan and add about 2 inches of neutral-flavor high-heat cooking oil. Heat the oil to 370°F.
Combine the dry ingredients. In a large bowl, combine the flour, 1/3 cup of sugar, baking powder, 1 teaspoon cinnamon, nutmeg, ginger, and salt. Stir or whisk to thoroughly blend the dry ingredients.
Combine the wet ingredients. In a small bowl, whisk the egg with the pumpkin and milk. Add the melted butterand vanilla and stir to blend.
Finish the batter. Pour the pumpkin mixture into the dry ingredients and stir until the flour is incorporated. Do not overmix.
Fry the fritters. Use a small cookie scoop or tablespoon to drop about 5 or 6 into the hot oil. Fry them for about 3 to 4 minutes, turning frequently, or until deep golden brown.
Drain the fritters. With a slotted metal spoon, transfer the fritters to paper towels to drain.
Finish with cinnamon sugar. Combine 1/4 cup of granulated sugar with 1 tablespoon of cinnamon in a wide bowl or plate. Roll the warm fritters in cinnamon sugar.