Preheat your oven to 325°F (163°C). Grease a 9x9-inch baking pan or line it with parchment paper for easier removal.
In a mixing bowl, combine the graham cracker crumbs, melted butter, and ¼ cup of sugar. Stir until the mixture resembles wet sand.
Press the crust mixture evenly into the bottom of the prepared baking pan. Bake in the preheated oven for 10 minutes. Remove and let cool while preparing the filling.
In a large mixing bowl, beat the softened cream cheese and 1 cup of sugar with an electric mixer on medium speed until smooth and creamy. Scrape down the sides as needed.
Add in the eggs one at a time, mixing well after each addition. Then, add the vanilla extract and sour cream, mixing until everything is well combined and smooth.
Gently fold in the raspberries or raspberry puree, creating a swirled effect in the cream cheese mixture without completely mixing it in.
Pour the cheesecake filling over the cooled crust, spreading it evenly.
Bake in the oven for 25 minutes, or until the edges are set but the center still has a slight jiggle. Remove from the oven and let cool at room temperature.
Once cooled, refrigerate the cheesecake bars for at least 4 hours (or overnight) before slicing into bars.
Cut into 12 equal bars and enjoy!