Heat a 10-inch nonstick skillet over medium-high heat until hot.
Add the thawed corn and cook, stirring occasionally, until kernels begin to brown, about 3 to 5 minutes; transfer corn to medium bowl.
Heat oil in skillet over medium heat until hot add the onion and cook, stirring occasionally, until softened, about 3 minutes.
Add garlic and chili powder and cook until fragrant, about 1 minute.
Stir in beans and cook until heated through, about 1 - 2 minutes.
Add the corn back to the skillet and toss to combine. Gently press mixture with spatula to lightly crush black beans.
Transfer mixture to now-empty bowl, add the lime juice in and toss to combine.
If needed, wipe out the skillet with paper towels and return pan to medium heat until hot, about 2 minutes.
Place 1 tortilla in skillet and sprinkle with a layer of cheese, a heaping scoop of the corn and bean mixture, and another light layer of cheese. Top with another tortilla.
Cook until the cheese is almost melted and the bottom tortilla is golden.
Use a large spatula to carefully flip the tortilla to the other side. Cook until cheese is melted and bottomo tortilla is golden brown.
Remove from pan, repeat making quesadillas three more times
Cut quesadillas in quarters and serve with as is or with sour cream and salsa.