Preheat oven to 375F. Butter and flour a 9×1½-inch round cake pan.
To make the cake:
In a medium bowl, whisk together flour, baking powder, baking soda, and salt making sure to remove any lumps. Set aside.
In a medium mixing bowl, beat the sugar and the butter with mixer on medium until fluffy. Add the egg and vanilla; beat on medium for another minute. Alternately add flour mixture and buttermilk to the sugar mixture, beating just until combined after each addition; set aside.
To make the cheesecake filling:
In a small mixing bowl, beat the cream cheese and sugar on medium until combined. Add lemon zest and egg; beat until combined
To assemble:
Spoon half the cake batter into prepared pan, spreading to edges. Pour the cheesecake filling on top and spread it to the edges. Spoon remaining batter on cheesecake filling and spread to the edges. Gently press raspberries into the cake.
Bake 50 – 55 minutes or until a toothpick inserted into the center comes out clean. Use a sharp knife to loosen the edges of the cake; remove from pan and cool on a wire rack.