In a mixing bowl, whisk together the flour, baking powder, cinnamon, nutmeg, salt, and granulated sugar until well combined.
In another bowl, mix the milk and egg together, then stir in the vanilla extract.
Pour the wet ingredients into the dry ingredients and mix until just combined. Fold in the chopped apples gently.
Heat about 2 inches of vegetable oil in a frying pan or deep fryer over medium heat.
Once the oil is hot, carefully drop spoonfuls of the batter into the hot oil. Fry in batches, making sure not to overcrowd the pan. Cook for about 2-3 minutes on each side or until golden brown.
Use a slotted spoon or tongs to transfer the fritter bites to a plate lined with paper towels to drain excess oil.
For the glaze, whisk together powdered sugar and milk in a small bowl until smooth. Adjust the consistency with more milk if too thick.
Dip each warm apple fritter bite into the glaze, allowing the excess to drip off, and place them on a cooling rack or plate to set.