To make the Zucchini Salsa: Add the corn kernels to a medium bowl. Add the zucchini, cilantro, jalapeno, lime juice, & olive oil. Season with salt and pepper and toss well to combine. Cover with a lid & refrigerate until ready to serve.
Brush one side of all tortillas with a small amount of butter; lay a tortilla, buttered side down, in a preheated skillet. Place a quarter of the filling on each tortilla, and sprinkle with a quarter of the cheese. Place the remaining tortillas on top, buttered side up; press down gently with a spatula to seal.
Saute until cheese has melted and tortillas are golden brown, turning once. Remove from the skillet & let cool slightly. To serve, slice each quesadilla into wedges.