Heat 1 teaspoon of the oil in a skillet over medium heat. Add the spinach and cook, stirring, until wilted, about 1–2 minutes; remove from heat and let cool slightly.
In a medium mixing bowl combine the cooked spinach, chopped chicken, eggs, flour, mozzarella, Parmesan, minced garlic, black pepper, chopped green onion, and salt; mix until evenly combined.
Heat the remaining oil (about 2 teaspoons) in a wide skillet over medium heat and grease the pan.
Spoon about 2 tablespoons of the mixture per fritter into the skillet and gently pat each into a 2–3 inch round.
Cook the fritters 2–3 minutes per side, until golden brown and cooked through, flipping carefully with a spatula; work in batches as needed so the pan isn’t overcrowded.
Transfer cooked fritters to a plate and serve warm with ketchup or mayonnaise, if desired.