Preheat oven to 350 degrees F. Lightly coat a 2-quart rectangular baking dish with cooking spray; set aside.
For orange sauce, in a small saucepan combine orange peel, orange juice, butter, sugar, and cinnamon sticks. Cook over medium heat just until mixture starts to boil. Pour mixture all at once into prepared baking dish.
For dumplings, on a clean, dry work surface, unroll crescent roll dough; separate into sections. Wrap each apple quarter with one section of the dough. Place in a single layer in prepared baking dish; spoon orange sauce over each dumpling.
Bake for 35 to 40 minutes or until golden, spooning sauce over dumplings halfway through cooking time. Cool for 15 minutes. Serve warm with whipped topping.