Welcome to the forum, Wilderful.
Usually the ailing peasants will turn up at the clinic, although sometimes you may have to wait for them to appear. Have you tried going to map view to see if there's a sim with a marker? With some quests, the sims you're looking for will congregate in the village square. I can't remember if that ever happened with this particular quest.
By the way, I edited your post to correct several spelling errors.