Line a baking sheet with parchment paper; set aside. On a lightly floured work surface, unfold pastry sheet; roll out to a 12-inch square. With a sharp knife or pizza wheel (and using a ruler as a guide, if desired), cut into four equal squares. Place on prepared baking sheet; refrigerate until firm, about 15 minutes.
In a medium bowl, stir together jam and raspberries.
Assemble turnovers: After chilling pastry squares, spoon jam mixture in center of each square. Using a pastry brush, dampen edges with water in a 1-inch border. Fold dough in half diagonally, over filling. Press edges to seal; with a fork, crimp to make a 3/4-inch border. Brush top of pastry with water; sprinkle with the sugar. With the tip of a paring knife, cut three small slits in the top (for steam vents).
Refrigerate until firm, about 30 minutes. Preheat oven to 375 degrees.while turnovers are chilling.
Bake until puffed and golden, about 25 minutes (some jam may bubble up through vents). Transfer baking sheet to a wire rack; cool. Serve warm or at room temperature.
Unbaked turnovers can be frozen for up to three months; freeze on the baking sheet until firm, about two hours, then transfer to resealable storage bags. Bake frozen turnovers on a baking sheet as directed in step 3, without thawing.