Melt butter in a pan over medium-high heat. Add the garlic and cook for 2 minutes while stirring. Add wine and cook for 3 minutes. Add the shrimp and cook each side for 3 minutes. Take off the heat and add the parsley and lemon juice. Salt and pepper to taste. Put cooked shrimp in a bowl and set aside.
Warm up tortillas in the microwave. Place 6 tortillas on a work surface to start building quesadillas.
Evenly divide cheese and corn between tortillas; place 4 shrimp over each. Sprinkle green onions on top and cover with another tortilla. Cook in a nonstick pan, flipping the tortillas over until each side is lightly brown, 4 to 5 minutes per quesadilla.