Make the marinade by mixing the peach preserves, honey, olive oil, mustard, lemon and lime juices, garlic powder, salt, and pepper in a small bowl; whisk to combine.
Place the marinade and drumsticks in a large resealable plastic bag and massage around the chicken to coat evenly. Refrigerate for 1 to 3 hours.
Preheat the oven to 450° F. Line a baking sheet with foil and spray with cooking spray.
Transfer the drumsticks and marinade to the prepared baking sheet. Bake until the chicken is golden and cooked through, 25 to 30 minutes.
Serve warm garnished with sliced peaches.
Time-Saver: In a pinch, simply pour on the marinade and bake.
Variation: This marinade works great on a roasted chicken, whole or cut into 8 pieces, as well.