To a medium saucepan over medium heat, combine filling ingredients and cook until apples are soft and syrup has thickened (about 10 minutes), stirring occasionally.
Transfer the apple mixture to a plate, and chill in the refrigerator to let cool, while preparing the puff pastry.
Divide puff pastry into 4 equal squares. Spoon a couple tablespoons of the apple filling onto the center of each square.
Prepare the egg wash by scrambling one egg with one Tbsp of water.
Brush egg wash on to the edges of each square. Fold each pastry square diagonally (creating a triangle) over apple filling, and seal with the edges with a fork.
Place the prepared turnovers on a plate and refrigerate while preparing the remaining second sheet of pastry turnovers. Repeat steps 4 to 6 for the second sheet of puff pastry.
Preheat air fryer to 325℉ (160℃)
Place apple turnovers in air fryer, brush tops with egg wash, sprinkle with sugar, and then make 3 small slits with a knife on the top of each turnover.
Cook in the middle rack until puffed and golden brown, about 20 minutes. Serve warm or at room temperature.