Peel and core the apples, then slice them into ½-inch pieces.
Mix the flour, sugar, baking powder, cinnamon, and ¼ teaspoon salt in a bowl.
Mix the milk and the egg into the dry ingredients, then stir in the chopped apples.
Mix the confectioner's sugar with 2 tablespoons of water to make the glaze.
Heat the oil in a deep skillet over medium-high heat.
Pour 2 tablespoons of batter into the hot oil for each fritter and cook for 2 minutes on each side — you should be able to fit 4 to 5 fritters per batch, so it will take 2 batches to use up the batter.
Set the fritters on a paper towel-lined plate to drain as they finish cooking.
Drizzle the fritters with the glaze before serving.