If the potatoes you unearth are too small to be useful then do not detach them from the main plant, gently cover them back up i.e. replace the soil around them and let them grow on for a while.
If you are unearthing some potatoes that are large enough to cook; gently remove them from the plant and leave the small immature potatoes still attached to grow on further. You can continue to do this until you are
ready to harvest the potatoes.
First earlies and salad potatoes taste best when freshly harvested so this is a nice way to gather your first few first early potatoes or salad potatoes for today or tomorrow's meal.