Thaw the pastry sheets, then unfold them and roll them out onto a cutting board or a very lightly floured surface, ensuring the seams are sealed.
Cut the pastry into strips approximately ½ inch wide using a pizza cutter or paring knife.
Prepare the apples by peeling and coring them, then slicing into pieces that are ¼ inch to ½ inch thick. Use a paring knife or a small round cookie cutter to enlarge the center hole of each apple slice to about 1 inch in diameter.
Brush the apple slices with lemon juice to prevent browning while you wrap them with the pastry strips.
Wrap each apple slice with 2-3 strips of puff pastry, looping them through the center.
Whisk together the egg white and a tablespoon of water, then brush the mixture onto the tops and bottoms of each wrapped apple slice. In a small shallow bowl, mix together the cinnamon and sugar, then dip each wrapped slice into the mixture, using a spoon to ensure both sides are coated.
Prepare the air fryer basket by lightly spraying it with nonstick cooking spray, or lining it with parchment paper or a silicone mat.
Arrange the coated apple slices in a single layer in the air fryer basket.
Air fry at 380°F for 6-8 minutes, or until the puff pastry is lightly golden brown. If necessary, turn the rings over and continue air frying for an additional 2-4 minutes until fully cooked.