Heat the oven to 400°F with a rack in the upper-middle position. Brush the cups and surface of a standard 12-cup muffin pan with oil. In a medium bowl, whisk together the flour, cornmeal, baking powder, baking soda and salt; set aside.

In a large bowl, combine the white sugar and lemon zest; rub together with your fingers until fragrant and begins to clump. Whisk in the ½ cup oil and eggs until well combined and slightly thickened, about 30 seconds. Whisk in the yogurt and lemon juice. Add the flour mixture and fold with a silicone spatula until just shy of incorporated. Scatter the raspberries over the batter and fold a few times. Add the jam and fold gently until the batter has a marbled appearance.

Scoop the batter into the cups of the prepared muffin pan, dividing it evenly. Sprinkle each with a scant ¼ teaspoon turbinado sugar. Bake until the muffins are golden brown and a skewer inserted into the centers comes out clean, 25 to 28 minutes, rotating the pan halfway through. Cool in the pan on a wire rack for 15 minutes. Lift the muffins out of the pan and set directly on the rack. Serve warm or at room temperature.