Preheat oven to 400, Line a baking sheet with parchment paper. Mix the apple, jam, and cornstarch in a bowl. Mix sugar, and cinnamon in another bowl.
On a slightly floured surface roll out pastry into an 8 by 12 inch rectangle. Cut into 6 - 4" squares.
Spoon some apple mixture into the center of each square, leaving a 1-inch border. Brush borders with beaten egg, fold each square into a triangle, press edges with a fork to seal tightly. Cut 2 small vents in top of each turnover. Sprinkle each turnover with cinnamon-sugar mix. Place turnovers on a lined baking sheet.
Bake until golden, and puffed, about 20 minutes.Serve warm.