In a roasting dish, combine chicken with lemon juice, olive oil, garlic, salt, pepper, and paprika. Cover and marinate in the fridge overnight or for at least 1 hour.
Preheat oven to 220°C (428°F). Bake the chicken for 30–35 minutes or until fully cooked. Let rest, then shred or slice.
For the fries, preheat a tray with oil in the oven for 10–15 minutes. Add fries in a single layer and bake for 30–40 minutes, flipping halfway. Once cooked, toss immediately with feta, zaatar, Aleppo pepper, salt, and black pepper.
In a bowl, whisk together yogurt, mustard, lemon juice, garlic, salt, and pepper to make the sauce.
To assemble, layer chicken, fries, yogurt sauce, parsley, and chili slices in warm bread. Roll or fold and serve immediately.