Peasants in my game worlds rarely have any real supernatural power. However, the social and technological state of things is closer to tail end of Early Modern period, rather than Medieval.

When peasants have "magic", it's of the "circle of salt wards off evil spirits" sort - a combination of superstition and use of talismans and natural materials against perceived supernatural threats. Some of these defenses are warranted, others less so. There are plenty of other weird beliefs and superstitions ("if you roll naked in rye during midsummer, you will see your future spouse!"), but those are nonsense. (People in real life have always been fond of nonsense and I see no reason for my fictional peoples to differ.)