In a large bowl, combine the ground chicken, Parmesan, mozzarella, zucchini, carrot, parsley, garlic, paprika, oregano, salt, and black pepper. Mix well.
In a separate bowl, whisk the eggs, mayonnaise, and flour until smooth. Add this mixture to the chicken filling and stir until fully combined.
Heat olive oil in a skillet over medium heat.
Scoop a spoonful of the mixture and shape it into a patty. Carefully place it in the skillet.
Cook each patty for about 3–4 minutes per side until golden brown and fully cooked through.
Transfer to a paper towel-lined plate to remove excess oil. Serve warm with your favorite dipping sauce.