Preheat the oven to 400 degrees F. Fill a regular-size muffin pan with paper muffin cups or spray with cooking spray. Set aside.
In a large bowl, whisk together the flour, cornmeal, sugar, baking powder, baking soda, and salt. Set aside.
In a medium bowl, whisk the buttermilk, melted butter, canola oil, and eggs until well blended. Pour the liquid ingredients over the dry ingredients and mix with a rubber spatula until combined. The batter will be lumpy. Fold in the zucchini, corn, and cheddar cheese. Divide the batter evenly among the muffin cups.
Bake for 15 minutes, or until the tops are golden and a toothpick inserted into the center of the muffins comes out clean. Transfer the pan to a rack and cool for 5 minutes. Remove muffins from pan and serve.