In a large bowl, combine the cooked chicken, chopped broccoli, cheddar cheese, breadcrumbs, eggs, Parmesan cheese, garlic powder, onion powder, salt, and black pepper. Mix until well combined.
Heat olive oil in a large skillet over medium heat.
Using a spoon or your hands, form the mixture into small patties, about 2-3 inches in diameter.
Once the oil is hot, add the fritters to the skillet, cooking in batches if necessary. Fry for about 3-4 minutes on each side or until golden brown and crispy.
Remove the fritters from the skillet and place them on a paper towel-lined plate to absorb excess oil.
Serve warm with your favorite dipping sauce.