Preheat the oven to 350°F and line a muffin tin with paper liners.
In a bowl, whisk together the flour, baking powder, baking soda, and salt.
In a separate bowl, cream the butter and sugar until light and fluffy. Beat in the eggs and vanilla, then add sour cream.
Gradually mix the dry ingredients into the wet until just combined.
Gently fold in the berries.
In a small bowl, mix cream cheese, sugar, and vanilla until smooth.
Fill muffin cups halfway with batter, add a spoonful of cream cheese mixture, then top with more batter.
Bake for 20–25 minutes or until a toothpick comes out clean. Let cool before serving.