Preheat the oven to 425°F (220°C) and line a baking sheet.
In a medium mixing bowl, combine the shredded chicken, corn, drained black beans, and enchilada sauce; toss until evenly coated.
Lay one tortilla on a work surface. Spoon about 1/4 of the chicken mixture onto half of the tortilla, spreading evenly.
Sprinkle about 1/4 cup of the Monterey Jack cheese over the chicken mixture, then top with about 1/4 of the chopped cilantro and 1 chopped green onion.
Fold the tortilla in half to enclose the filling and gently press down to flatten; repeat to make the remaining three quesadillas.
Arrange the folded quesadillas on the prepared baking sheet and bake for about 8–10 minutes until the tortillas are crisp and the cheese is melted, flipping halfway if your oven browns unevenly.
Remove from the oven, let rest briefly, cut each quesadilla in half, and serve with sour cream or guacamole if desired.