Preheat the air fryer to 400 degrees F (200 degrees C) for 5 minutes.
Combine flour, sugar, baking powder, apple pie spice, and salt in a large bowl. Whisk together.
Combine applesauce, sparkling apple cider, melted butter, egg, and vinegar in a small bowl; whisk until well combined. Add wet ingredients to the dry ingredients using a spatula and blend until just combined. Using a spring-hinged ice cream scoop, fill each individual cavity of the silicone donut mold with 2 tablespoons batter. Place mold into the air fryer basket.
Decrease temperature to 350 degrees F (175 degrees C) and cook for 8 minutes. Carefully turn out the donut bites and cook for an additional 2 minutes.
Remove donut bites from the basket when done and let cool completely on a wire rack before glazing, about 30 minutes.
Combine powdered sugar and apple pie spice in a small bowl and whisk together. Add sparkling apple cider and caramel extract; whisk together until the glaze is smooth.
Dip each donut bite into the glaze, rolling it so that all sides are covered with the glaze. Set on a wire rack to allow the glaze to dry and harden before eating.