In a large bowl, stir together the flour, cornmeal, 2 tablespoons sugar, baking powder, salt and cinnamon. In a medium bowl, combine egg whites, apple, and milk. Add to flour mixture all at once and stir just until combined.
In a deep, 12-inch cast iron skillet, heat 1 inch vegetable oil over moderate high heat, to 375º or until a 1-inch cube of bread browns in 30 seconds.
Carefully drop the batter by heaping tablespoons, several at a time, into hot oil. Cook for 3 to 4 minutes or until golden brown, turning once. Using a slotted spoon or wire mesh ladle, remove and drain on paper towels.
In a paper bag, combine 1/3 cup sugar and nutmeg. Add the hot fritters, several at a time, and shake to coat.