Bake the sweet potatoes until done but still firm. Plunge into a bowl of ice water.
Cut the narrow part of the squash into thin rounds. Cut the wider part of the squash in half, then slice thinly.
Combine the squash with a small amount of water in a medium skillet; cover and steam until partially done, about 2 minutes. Add the corn kernels and continue to steam until the squash is tender-crisp, then remove from heat.
Peel the sweet potatoes and mash them.
Lay a tortilla on a baking sheet. Spread mashed sweet potato over one half, followed by a quarter of the squash and corn mixture. Sprinkle with 1/2 cup cheese. Fold over to cover. Repeat with the remaining tortillas, using an additional baking sheet if needed.
Bake for 10 minutes, or until the tortillas begin to turn golden and crisp. Watch carefully!
To serve, place each quesadilla or half of quesadilla on an individual plate. Serve at once, passing the salsa to top individual portions.