Preheat oven to 450 degrees F. Spray sheet pan well with cooking spray. Reserve 1-1/2 teaspoons of fajita seasonings for dressing.
Slice peppers and onions into 1/4" to 1/2" spears. If using hot peppers, slice in rounds to differentiate spicy from regular peppers.
Place peppers and onions in large bowl, and toss with 1 tablespoon of oil. Sprinkle on 1 tablespoon of fajita seasoning and toss to coat. Spread evenly over sheet pan.
Repeat coating with chicken: toss pieces in large bowl with oil then sprinkle with remaining fajita seasoning. Spread over top of peppers and onions in sheet pan.
Cook peppers, onion and chicken in bottom 1/3 of oven, tossing occasionally, until onions and peppers begin to brown and chicken reads 160 degrees when tested with a meat thermometer.
Meanwhile, place salad greens in serving bowl and sprinkle with shredded cheese. Toss well.
Prepare dressing: combine ranch dressing and reserved fajita seasoning in small bowl.
When chicken is cooked thoroughly, top salad greens with baked mixture. Add dressing and mix again. Serve immediately.