Preheat the oven to 400°F (200°C).
Place the chicken leg quarters and potato wedges in a large baking dish.
In a small bowl, whisk together the olive oil, lemon juice, minced garlic, dried oregano, salt, black pepper, paprika, and cayenne pepper.
Pour the marinade over the chicken and potatoes, making sure they are evenly coated.
Bake in the preheated oven for 1 hour, or until the chicken is cooked through and the potatoes are golden brown and crispy.
Serve hot and enjoy!