In a small bowl, combine the Greek yogurt, light mayonnaise, jalapeño juice, garlic powder, paprika, cumin, and salt to make the creamy jalapeño sauce.
Add half of the sauce to the shredded chicken and stir to coat.
Divide the chicken mixture evenly among the tortillas and top with cheese. Fold each tortilla in half.
Heat a large nonstick skillet over medium heat.
Cook the quesadillas for 2-3 minutes per side, or until golden brown and the cheese is melted.
Slice into wedges and serve with the remaining sauce for dipping.