Preheat oven to 350 degrees F. Line 12 muffin cups with paper liners. Set aside.
In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside. In a small bowl, add the sugar and lemon zest. Rub the lemon zest and sugar together with your fingers. Using an electric mixer, beat the butter and sugar and lemon zest mixture together until light and fluffy, about two minutes. Add the ricotta cheese and beat until smooth. Beat in the egg, lemon juice, and vanilla extract.
Add the dry ingredients and mix until just blended. Using an ice cream scoop or large spoon, fill each muffin cup half way with batter. Add three blackberries to each muffin cup. Top the muffins with remaining batter so blackberries are covered. Generously sprinkle turbinado sugar over each muffin top.
Bake muffins for about 20-25 minutes, or until the tops are slightly golden brown. Let muffins cool for five minutes and serve.