Preheat your oven to 350°F. Line two baking sheets with parchment paper.
In a large mixing bowl, cream together the softened butter and granulated sugar until light and fluffy, about 3-4 minutes.
Add the egg and vanilla extract to the mixture, and beat until well combined.
In a separate bowl, whisk together the flour, baking powder, and salt. Gradually add the dry ingredients to the wet mixture, mixing until just combined.
Using a tablespoon, scoop out the dough and roll it into balls. Place the balls on the prepared baking sheets, spacing them about 2 inches apart.
Using your thumb or the back of a teaspoon, make an indentation in the center of each dough ball. Fill each indentation with a teaspoon of raspberry jam or blueberry jam.
Sprinkle the tops of the cookies with red, white, and blue sprinkles.
Bake in the preheated oven for 12-15 minutes, or until the edges are lightly golden. Allow the cookies to cool on the baking sheets for 5 minutes before transferring them to a wire rack to cool completely.