Preheat oven to 350 degrees F (175 degrees C). Spray an 8x13-inch baking dish with cooking spray.
In a large bowl, lightly mix together the peach, nectarine, and plum slices until well mixed, and toss with the cornstarch to dust the fruit. Pour in the currant jelly, apple pie spice, and white pepper, and lightly mix again with your hands to coat the fruit with the jelly and seasonings. Spread the fruit into the prepared baking dish.
Pop open the can of biscuits, and cut them in half. Arrange the biscuit dough halves on top of the fruit. Mix the sugar and cinnamon in a small bowl, and sprinkle the mixture evenly on the biscuit dough.
Bake in the preheated oven until the biscuits are golden brown, 20 to 25 minutes. Allow to cool on a rack for at least 20 minutes to let the dish set up.