Preheat the oven to 375 degrees F (190 degrees C). Spray a nonstick muffin pan with cooking spray or rub with oil.
Place shredded zucchini and potato in a cheesecloth and wrap cloth over the vegetables. Over a bowl, squeeze vegetables to remove as much water as possible. Open up the cheesecloth, and squeeze handfuls of vegetables to extract more water, then place back in the cheesecloth to rest.
Add drained vegetables, Parmesan cheese, flour, eggs, onion, garlic powder, onion powder, salt, black pepper, and paprika to a bowl; stir to combine thoroughly. Fill muffin cups about 3/4 full with the mixture.
Bake in the preheated oven until golden brown and a toothpick inserted near the middle comes out clean, 20 to 25 minutes. Let sit for 5 minutes, then remove from the muffin pan.
