If the green potato plant above the soil stays small in size the problem may be soil fertility - improve it. If the seed potatoes rot in the soil where you planted them, they may be infected. Where did you get your seed potatoes? Or your soil may be infected with pathogens - what grew in it before? Or it may be water-logged, promoting infection, in that case you need to improve the soil texture, make it drain better. Clay is bad for potatoes. There are many possibilities and your description is not very specific. Also, your new potatoes can be any size, I am not sure what size you expect them to be.