In a large bowl toss ham, corn, chili powder and cheese.
Heat 10-inch nonstick skillet over medium-high heat.
Place one flour tortilla in skillet; layer with about 1/2 cup of the ham mixture to within 1/2 inch of edge of tortilla. Top with another tortilla.
Cook over medium-high heat for 4 to 5 minutes, turning after 2 minutes, until light golden brown.
Remove quesadilla from skillet and keep warm.
Repeat with remaining tortillas and filling.
Cut quesadillas into wedges to serve.
Serves 4 to 5