Cut chicken and vegetables into thin strips and place in two separate zip top bags - one for chicken and one for vegetables. Add olive oil, lemon juice, chili powder, ground cumin, cayenne pepper, salt, pepper, and garlic to a jar with a screw top or tight fitting lid. Shake until well combined. Pour ⅓ over chicken, ⅓ over vegetables and reserve the remainder in the jar for using when cooking the chicken fajitas. Seal zip top bags tightly and refrigerate for one hour to overnight.
When ready to cook, heat skillet over medium heat. Pour vegetable bag into the skillet and saute. Remove to a plate when cooked through and add chicken strips to the same skillet. When almost completely cooked throughout, add vegetables back to the skillet along with the reserved marinade.
For Quesadillas:
Place tortilla in large skillet or griddle over medium heat. Spread shredded cheeses over the top of the tortilla. Pile chicken fajita ingredients onto one side of the tortilla. Allow to cook until the cheese begins to melt and the tortilla is lightly browned. Fold the tortilla over to enclose the chicken fajita ingredients. Serve.