Heat a skillet over medium-high heat. Place tortilla onto skillet and top with Oaxaca cheese. Drizzle on Buffalo sauce and ranch dressing. Place chicken one half of the tortilla and cook until cheese is melted, 2 to 4 minutes.
Fold the tortilla in half, enclosing the filling. Flip once in the pan, and cook until both sides are golden brown, about 3 minutes more.
Remove from skillet and cut quesadilla into 4 triangles.
