Season shrimp with chili powder, smoked paprika, salt, and pepper.
Heat olive oil in a skillet over medium-high heat. Sauté shrimp until pink and opaque, about 2–3 minutes per side. Remove and set aside.
In the same skillet, sauté onions and jalapeños until soft and fragrant, 3–4 minutes.
Place a tortilla on a flat surface, sprinkle half the cheese over one side, layer shrimp, onions, jalapeños, and remaining cheese. Fold the tortilla over.
Heat butter or oil in a skillet over medium heat. Cook quesadilla 2–3 minutes per side until golden and cheese is melted.
Repeat with remaining tortillas.
Slice into wedges and serve immediately.