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