Heat the oven to 425°F. Line a rimmed baking sheet with parchment paper. Lightly grease 8 cups of a standard muffin pan.
Cut the potatoes lengthwise into wedges. Toss them with the olive oil and dry ranch seasoning, then arrange them in a single layer on the baking sheet with the cut sides facing down.
In a large bowl, combine the ground chicken, breadcrumbs, egg, celery, onion, ¼ cup of the buffalo hot sauce, garlic powder, paprika, salt, and black pepper. Mix gently just until combined.
Divide the chicken mixture among the 8 prepared muffin cups, filling each cup evenly. Brush the tops with the remaining buffalo hot sauce.
Put the potato wedges in the oven and bake for 15 minutes. Add the muffin pan to the oven and bake both for another 18 to 22 minutes. The muffins are ready when the centers reach 165°F. Turn the wedges once during baking so they brown evenly.
Let the muffins rest in the pan for 5 minutes. Serve them with the ranch-baked potato wedges, crumbled blue cheese, and ranch dressing.