Preheat oven to 350 degrees F (175 degrees C). Line 2 baking sheets with parchment paper.
Roll out 1 puff pastry sheet on a floured work surface until it is 1/4-inch thick. Cut into 16 squares. Transfer to a baking sheet and prick all over with a fork. Repeat with remaining puff pastry sheet.
Bake in the preheated oven until lightly browned on the top and bottom, 10 to 15 minutes. Let cool, about 10 minutes.
Combine cream cheese, white sugar, heavy cream, and lemon zest in a bowl. Mix by hand until smooth and glossy. Dollop cream cheese mixture over 16 squares. Spread out cream cheese mixture and cover with raspberries. Top with the remaining puff pastry squares and dust with confectioners' sugar.