Mix Greek yogurt with lime juice, remaining salt, and adobo sauce; set aside.
Assemble quesadillas: sprinkle cheese on tortillas, add chicken mixture, top with cheese, then fold.
Cook quesadillas in oiled skillet 3-4 minutes per side until crispy and cheese melts. Rest, then cut into thirds and serve with cilantro and yogurt sauce.
Notes
Use fresh ingredients for best flavor. Adjust spice levels to taste.