Preheat your oven to 400°F. Line two large baking sheets with parchment paper and set them aside.
On a lightly floured surface, cut each puff pastry sheet into 6 equal rectangles to get 12 rectangles, each approximately 4½x3 inches.
Place the pastry rectangles onto the prepared baking sheets, leaving about 1 inch of space between each piece.
With a fork, poke a few holes in the center of each pastry, leaving a ½-inch border around the edge to help the edges puff while keeping the center flat.
In a medium bowl, mix together the softened cream cheese, white sugar, and almond extract until well blended.
Spoon a generous tablespoon of the cream cheese mixture into the center of each pastry rectangle.
Spoon about 2 heaping tablespoons of cherry pie filling on top of the cream cheese mixture.
In a small bowl, whisk the egg and water together. Brush this egg wash around the outer edges of each pastry rectangle.
Bake in the preheated oven for 15 to 18 minutes or until golden.
Remove from the oven and lightly dust with powdered sugar. Let cool slightly before serving.