In a 1 1/2-quart saucepan, combine the shredded chicken, sliced green onions, chili powder, granulated sugar, smoked paprika, ground cumin, garlic powder, and cayenne pepper. Stir in the water to moisten the mixture. Cook over medium heat for 2 to 3 minutes, stirring occasionally, until the mixture is thoroughly heated.
Place one tortilla on a flat surface. Spoon 1/2 cup of the chicken mixture onto one half of the tortilla. Arrange 1/4 of the sliced avocado over the chicken. Drizzle 1 teaspoon of lime juice over the avocado. Sprinkle 1/4 cup of shredded cheddar cheese on top. Fold the tortilla in half to cover the filling and press gently to seal.
Heat 1/2 teaspoon of vegetable oil in a 12-inch nonstick skillet over medium-low heat. Once the oil is hot, place one quesadilla in the skillet. Cook for 2 to 3 minutes on each side, or until the tortilla is golden brown and the cheese has melted. Remove from the skillet and set aside. Repeat with the remaining quesadillas.
Cut each quesadilla into wedges and serve immediately. Garnish with a dollop of Daisy Sour Cream on the side for dipping.