To make the anchovy dressing, place the yogurt, mustard, lemon juice, chili, anchovy, mint, salt, and pepper in a bowl. Mix to combine and set aside.
Preheat oven to 400°F. Heat the oil in a large non-stick frying pan over high heat. Add the capers and cook for 2–3 minutes or until crispy. Remove with a slotted spoon and set aside. Sprinkle the chicken with salt and pepper and cook, skin-side down, for 3–4 minutes or until golden. Transfer to a baking tray lined with non-stick baking paper and roast for 12–15 minutes or until golden and cooked through.
Place the zucchini, apple, and fennel in a bowl, drizzle with the dressing and toss to combine. Slice the chicken and divide between serving plates with the salad. Top with the crispy capers to serve.