Place grated zucchini in a clean kitchen towel or paper towels and squeeze it tightly with your hands to remove excess water.

Place drained zucchini in a medium bowl; add eggs, flour, Parmesan cheese, mozzarella cheese, onion, and salt and stir until well combined.

Heat oil in a skillet over medium-high heat.

Scoop tablespoonfuls of zucchini mixture into hot oil and fry, working in batches, until crisp and golden brown, about 2 minutes per side.