Fill a heavy bottomed pot with about 2 inches of vegetable oil and heat over medium heat until a deep fry thermometer reaches 350°F (175°C).
While the oil is heating, combine the flour, granulated sugar, baking powder, ground cinnamon and salt in a large mixing bowl.
Add the milk, eggs and vanilla extract to the dry ingredients and stir until combined to form a thick batter.
Fold in the finely diced apples using a rubber spatula until evenly distributed throughout the batter.
Drop rounded tablespoonfuls of the batter into the hot oil, frying 4 to 5 bites at a time so as not to overcrowd the pot.
Fry for 2 to 3 minutes on each side, turning once, until they are puffy and golden brown all over.
Remove the fritters from the oil with a slotted spoon or spider strainer and place on a wire rack set over a baking sheet.
Whisk together the powdered sugar, milk and vanilla extract in a small bowl until smooth.
Drizzle the sweet glaze generously over the warm fritter bites and let sit for a few minutes before serving.