Preheat the oven to 400°F (200°C). Grease a large baking sheet with cooking spray or a light coat of olive oil and set aside.
Place the chicken breasts in a zip-top bag or large bowl and add the fajita seasoning; toss or shake until the chicken is fully coated.
Heat 1 tablespoon olive oil in a large heavy-duty skillet over medium-high heat for about 2 minutes.
Add the seasoned chicken to the hot skillet and cook 5–6 minutes per side, until cooked through and internal temperature reaches 165°F (74°C). Remove and let rest 4–5 minutes, then chop into small pieces.
Using the same skillet, add the sliced onion and bell pepper and cook on high heat 2–3 minutes, stirring, until they are softened and lightly charred.
Place the 8-inch tortillas on the prepared baking sheet. On one half of each tortilla, divide the chopped chicken (about 1/4 of the mixture), the sautéed peppers and onions (about 1/4 of the mixture), and 1/4 cup shredded cheese.
Fold each tortilla in half to enclose the filling. Lightly spray both sides with cooking spray or olive oil spray.
Bake for 10 minutes, flip the quesadillas, then bake another 10 minutes until golden and crispy and the cheese is melted.
Remove from the oven and serve immediately with desired dips such as salsa, sour cream, or guacamole.