To make the chicken. In a 9 x 13-inch baking dish, combine the yogurt, olive oil, lemon juice, garlic, paprika, oregano, and a pinch each of salt and black pepper. Add the chicken and toss to coat. Cover and marinate in the fridge for at least 1 hour or up to 12 hours.Preheat the oven to 425 degrees F. Remove the chicken from the fridge and let it sit at room temperature while the oven preheats. Transfer the chicken to the oven and roast for 20 to 25 minutes, or until the chicken is cooked through. Remove the chicken from the oven and let cool for 5 minutes. Shred the chicken with two forks or thinly slice it.Meanwhile, make the fries. In a small bowl, whisk together the olive oil, garlic, oregano, cayenne, and salt and black pepper to taste. Place the potato matchsticks in a large bowl and pour over half the garlic mixture. Gently toss to coat. Divide the fries between two baking sheets, arranging them in a single layer. Bake for 15 to 20 minutes, then flip, reduce the oven temperature to 400 degrees F, and bake for 15 to 20 minutes more. Remove from the oven and toss with the remaining garlic mix and the feta. Stuff the chicken inside the warm naan and serve with the fries, tzatziki, pickled red onions, and radishes, if desired.