What is incumbent upon one afflicted with obsessive doubts concerning prayers already performed, if he discovers, after ritual bathing, a small particle adhering to a limb, and he does not recall whether it was present before the ghusl or not?

You must turn away from misgivings and not pay attention to them, because succumbing to them leads to great evil. It is not necessary to repeat the ghusl if you find a barrier after purification and do not know whether it occurred before or after; the default is that it occurred after. Furthermore, a slight barrier does not invalidate purification according to some scholars, and it is permissible for someone afflicted with misgivings to adopt this view.