Pull Oaxaca cheese into strings (as if you were eating string cheese) into thin threads. If the Oaxaca cheese is in a circle, unravel the circle to one long rope of cheese, then pull into threads.
Stir together 2 cup shredded cooked chicken, 1 1/2 teaspoons chili powder, 1 teaspoon onion powder, 1 teaspoon garlic powder, 1/2 teaspoon kosher salt, 1/4 teaspoon freshly ground black pepper in a medium bowl.
Heat a large frying pan over medium-high heat. Lay 1 flour tortilla in the pan and spread about 1/2 cup of Oaxaca cheese on one half of the tortilla. Top with about 1/2 cup of the chicken, a few apple slices and about 1 teaspoon of salsa. Finish with another 1/2 cup of the cheese and fold the tortilla over to close.
Cook until one side is toasted and golden brown and the cheese is starting to melt. Flip and toast the other side until the cheese is completely melted.
Continue with the remaining ingredients to make 3 more quesadillas.
Cut each quesadilla in half and serve with sour cream, more salsa, diced avocado, thinly sliced jalapeños, chopped cilantro and lime wedges.