Preheat the oven to 400°F. Line 2 large baking sheets with parchment paper and set aside.
Lay the puff pastry sheets on a lightly floured surface, and cut each sheet into 6 equal-sized rectangles. You will have a total of 12 rectangles, about 4½x3 inches in size.
Arrange the puff pastries evenly onto the lined baking sheets, leaving about 1 inch between each pastry.
Use a fork to poke a few holes into the middle of the pastry sheet. Be sure to leave about a ½-inch perimeter around the edge. This will allow the outside border to puff up while the center stays low and holds the filling.
In a medium bowl stir together the cream cheese, sugar, and almond extract until fully combined.
Spread 1 heaping tablespoon of the cream cheese mixture onto the center of each puff pastry.
Top the cream cheese mixture with 2 heaping tablespoons of cherry pie filling.
In a small bowl, whisk the egg and water together. Brush onto the outside edges of the pastry.
Bake for 15-18 minutes, or until golden.
Remove from oven and dust with confectioners' sugar. Set aside to cool slightly before serving.