Preheat the oven to 400 degrees. Spray a 24-cup mini-muffin pan with cooking spray.
Place the shredded zucchini in a medium-sized bowl and toss with the salt. Let sit for 10 to 15 minutes. Squeeze out any moisture and discard the liquid.
Sprinkle the coconut flour onto the zucchini and toss well to coat. Add the eggs, cheddar cheese, onion, and paprika and mix well to combine.
Fill each muffin cup with 1.5 tablespoons of the zucchini mixture. Bake for 15 minutes, or until golden brown. Run a knife around the tots to loosen as soon as you get them out of the oven. Let cool for a minute to allow them to set up, then remove them from the muffin pan.