Drain shredded zucchini of excess moisture. Toss with coconut flour. Add eggs, Cheddar cheese, onion, and paprika. Scoop mixture into muffin cups.
Bake for 15 minutes in the preheated oven, or until golden brown. Let cool for a minute to allow them to set up, then remove them from the muffin pan.
Four tots have 115 calories, 7 grams of protein, and only 3 net grams of carbohydrates.