Preheat the oven to 350 degrees F (175 degrees C). Spray 24 muffin cups with cooking spray or line with paper liners.

Whisk sugar, oil, eggs, and vanilla extract together in a bowl until smooth. Stir flour, cinnamon, baking soda, and baking powder into sugar mixture just until batter is combined; fold in shredded zucchini and apple.

Spoon batter into the prepared muffin cups, filling each 2/3 full.

Bake in the preheated oven until until muffins spring back after pressing the top, about 25 minutes.