In a bowl, mix shredded chicken, buffalo sauce, ranch dressing, garlic powder, black pepper, cheddar, and mozzarella until well combined.
Warm tortillas slightly to make folding easier.
Place tortilla on a flat surface and cut a slit from the center to one edge.
Divide filling into sections and place on one quadrant of the tortilla.
Fold tortilla in sections into a layered square wrap.
Heat butter or oil in a skillet over medium heat.
Place wrap seam-side down and cook for 2–3 minutes per side until golden and crispy.
Press lightly with spatula for even browning.
Remove, rest for 1–2 minutes, and serve warm with dipping sauce.