Combine enchilada sauce, water, and taco seasoning in a slow cooker. Cut chicken breasts in half lengthwise and add to the slow cooker. Cook on Low until chicken is tender, 4 to 5 hours.

Remove chicken and shred using 2 forks. Return chicken to sauce in the slow cooker; mix well.

Spoon some of the chicken mixture onto a tortilla. Sprinkle some of the cheese on top. Cover with another tortilla.

Heat a large nonstick skillet over medium heat. Slide quesadilla into the hot skillet. Cook until browned on both sides, 2 to 4 minutes, flipping halfway through. Repeat with remaining tortillas, chicken, and cheese.