In a large bowl, whisk together the flour, granulated sugar, baking powder, cinnamon, nutmeg, and salt.
In a separate bowl, whisk together the egg, milk, melted butter, and vanilla extract. Pour the wet ingredients into the dry ingredients and stir until just combined. Fold in the diced apples gently. The batter will be thick and slightly lumpy.
Preheat the air fryer to 350°F (175°C) for 3 minutes. Line the air fryer basket with parchment paper and spray with cooking spray.
Using a large spoon or cookie scoop, drop roughly 1/4 cup mounds of batter onto the parchment paper, spacing them apart. Flatten each mound slightly with the back of the spoon. Spray the tops lightly with cooking spray.
Air fry at 350°F for 8 to 10 minutes, flipping halfway through, until the fritters are golden brown and cooked through in the center.
While the fritters cook, whisk together the powdered sugar, milk, and vanilla extract until smooth to make the glaze.
Let the fritters cool for 3 minutes, then drizzle or dip them generously in the glaze. Let the glaze set for a couple of minutes before serving.