Cut the chicken into small pieces about 1/8 inch in size and set aside.
In a medium bowl, whisk together the eggs and buttermilk until combined.
In a large bowl, combine the flour, salt, pepper, paprika, and garlic powder and whisk to mix.
Pour the egg mixture into the dry ingredients and stir until a batter forms.
Fold the chopped chicken, shredded mozzarella, shredded cheddar, and sliced green onions into the batter until evenly distributed.
Heat about 1 inch of vegetable oil in a large skillet over medium-high heat until shimmering and hot.
Drop batter by roughly 1/4-cup scoops into the hot oil, spacing the fritters so they do not touch, and fry 4–5 minutes per side until golden brown and cooked through.
Transfer fritters to a paper towel–lined plate to drain briefly before serving.