Mix together the shredded chicken, buffalo sauce, green onions, ranch dressing, onion powder, garlic powder, and black pepper in a large bowl.
Working in batches of 2, melt ½ tablespoon butter in a large nonstick skillet over medium-high heat.
Layer half of each tortilla with ¼ cup shredded cheese, ½ cup shredded chicken mixture, and another ¼ cup shredded cheese. Fold it over and cook the quesadillas in the skillet for 1 to 2 minutes per side until the cheese has fully melted and the quesadillas are golden brown. Repeat with the remaining tortillas.
Serve with sour cream, Mexican crema, or ranch dressing.