Pat the chicken dry and place in a large bowl. Add two tablespoons of oil and toss to coat.
Mix the paprika, coriander, garlic, onion, allspice, cinnamon, salt and pepper together in a small bowl. Remove one tablespoon of the spice mixture and set it aside.
Sprinkle two tablespoons of the mixture over the chicken and toss to thoroughly coat.
Place the chicken thighs on a sheet pan. Add the squash cubes and fingerling potatoes to the bowl. Drizzle with one tablespoon of oil and toss to coat.
Add the remaining spice mixture and toss to coat. Pour the vegetables onto the baking sheet around the chicken thighs.
Place in the oven and roast until the chicken is cooked through and the vegetables are fork tender, about 25 minutes.
Transfer to a serving platter and serve immediately.