Unroll the puff pastry sheets and cut each evenly into 4 squares. To assemble, roll out 1 square of puff pastry with a rolling pin into at least a 5-by-5-inch square. Place 3 tablespoons apple pie filling in the center and fold the pastry over to form a triangular pocket. Use a fork to crimp the edges. Repeat with the remaining puff pastry squares and apple filling.
Spray the waffle iron with nonstick cooking spray. Place 1 turnover into each of the 4 square areas on the waffle iron. Close the top and cook for 4 1/2 to 5 minutes; the pastry will be golden brown and toasted. Repeat with the remaining turnovers.