Line a rimmed baking sheet with paper towels in preparation for draining fritters once they are cooked.
Whisk together flour, baking powder, sugar, salt, and apple pie spice in a medium bowl. Add diced apples and toss in the flour mixture. Whisk together milk, eggs, and vanilla in a 2-cup measuring cup. Stir carefully into flour mixture with a rubber spatula, just until well-combined.
Pour oil into deep skillet or Dutch oven over medium heat and bring to 350º F. Using two tablespoons, place 5 to 6 scoops at a time into heated oil. Cook apple fritters about 3 minutes on each side until golden brown and cooked through.
Remove from the Dutch oven with a slotted spoon and place onto prepared pan for draining.
For the glaze:
Whisk together confectioner's sugar, milk, and apple cider until smooth. Spoon 1 teaspoon of glaze over each apple fritter and allow to rest about 8 to 10 minutes before serving.