Hi, Without seeing a sample of your peach I can't be sure of what's happening because there are several maladies that can cause small spots on dwarfed fruit. You also don't mention if the foliage has any spots or shows any yellowing. That can often help identify the problem. Some of the ailments that come to mind include Scab, Shot-Hole Fungus or Bacterial Leaf Spot. I would take a sample of the fruit AND foliage to your local garden center or extension service to get an up-close examination. Sorry I can't help more, but I don't have enough information here to go on.