Combine all the ingredients: mashed pumpkin, flour, baking powder, sugar, milk, cinnamon, nutmeg, allspice, salt, and egg in a large bowl. Stir until everything has been fully combined.
Pour vegetable oil into a saucepan until it’s at least 3 inches (or about 8 centimeters) deep. If the oil isn’t deep enough, the fritters will flatten slightly. Heat over medium heat until the oil is 350℉ (180℃).
The dough will be sticky and light. Grab a little bit of mixture with your hands or scoop it up with a spoon, and gently drop it into the oil. Repeat until all the batter is used up. You’ll probably need to do this in batches to avoid overcrowding the pan.
Fry for 2-3 minutes until it is golden brown. Remove them from the oil with a slotted spoon and drain them on paper towels to soak up excess oil.
If desired, roll the hot fritters in cinnamon sugar or drizzle them with the caramel glaze.