Melt 1 tablespoon of butter and 1 tablespoon of olive oil in a skillet over medium heat. Stir in the bell pepper and green onions; season with fajita seasoning and cayenne pepper. Cook and stir until the bell pepper is nearly tender, about 4 minutes. Add the crawfish tails and cook a few more minutes until hot and set aside.
Place the tortillas onto your work surface; divide about half of the queso fresco onto one side of each tortilla. Evenly divide the crawfish mixture on top of the cheese, then sprinkle with the remaining cheese. Fold the tortillas over the filling, pressing down lightly.
Melt 1 teaspoon of butter and 1 teaspoon of olive oil in a large skillet over medium heat. Place two of the quesadillas into the skillet, and cook until golden brown on each side, about 3 minutes per side. Repeat with the remaining butter, olive oil, and quesadillas. Cut into wedges to serve.