Place sweet potatoes into a large pot and cover with salted water; bring to a boil. Reduce heat to medium-low and simmer until very tender, about 15 minutes. Drain and transfer to a bowl. Mash sweet potatoes and mix in cilantro, chili powder, and salt.

Place corn in a microwave-safe bowl and microwave on high until warmed, 1 to 2 minutes.

Spread 1/4 cup sweet potato mixture onto 1 tortilla; cover with 1/4 cup black beans and 1 tablespoon corn. Sprinkle 1/4 cup Cheddar cheese atop corn; cover with a tortilla. Repeat with remaining tortillas and fillings.

Spray a frying pan with cooking spray and place over medium heat; cook 1 quesadilla in the hot pan until cheese is melted and beans are heated through, 3 to 4 minutes per side. Repeat with remaining quesadillas; slice into quarters.