Preheat oven to 325°F (165°C). Line a 9-inch square baking pan with parchment paper, letting excess extend over sides of pan.
In a medium bowl, stir together graham cracker crumbs, 1/4 cup sugar, and melted butter until well combined. Press mixture firmly into the bottom of the prepared pan.
Bake crust for 10 minutes. Let cool slightly.
In a large bowl, beat cream cheese with a mixer on medium speed until smooth. Add 3/4 cup sugar and flour, beating until combined.
Add eggs, one at a time, beating well after each addition. Beat in sour cream and vanilla until smooth.
Pour cream cheese mixture over the prepared crust, smoothing the top.
Drop small spoonfuls of raspberry preserves over the filling. Using a knife, gently swirl to create a marbled effect.
Bake until center is set, 35 to 40 minutes. Let cool completely on a wire rack. Refrigerate until firm, at least 2 hours or overnight.
Use parchment paper to lift bars from pan before cutting into squares.