Among the followed means in my society in seeking cure is going to the shrines of the righteous people. Some people claim that whoever is afflicted with paralysis or any other disease has only to stay overnight at the shrine of a certain Shaykh. Moreover, someone claims that he knows a person who was paralyzed and spent the night at one of these shrines and in the morning of the next day he was healed and could walk on his own.
What is the ruling under Sharee‘ah on these claims? How can we convince them that their acts are invalid and that only Allah can heal them?
May Allah Reward you.

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.

There is no doubt that asking anyone other than Allah and seeking relief or healing from him is an act of major Shirk that contradicts Tawheed. Allah The Almighty Says (what means): {And do not invoke besides Allah that which neither benefits you nor harms you, for if you did, then indeed you would be of the wrongdoers.} [Quran 10:106] “Wrongdoers” here means the “polytheists.”

Shaykh Al-Islam Ibn Taymiyyah said, “…one of its (Shirk) forms is to ask him (shrine dweller) to heal him or his animals; to pay off his debt; to take revenge for him from an enemy; or to grant him, his family and animals well-being; and other matters that none but Allah The Almighty Can do. Then, this is a clear act of Shirk whose doer must be asked to repent to Allah and to shun this act. If he does not repent, he should be killed.”

The supernatural events that sometimes happen at the shrines are done by devils to be a trial for them and other people of weak faith who have little religious knowledge.

Ash-Shaatibi said, “The supernatural acts that contradict Sharee‘ah are proof for the invalidation of these acts. They may appear like the supernatural matters that happen to righteous people but they are the works of Satan.”

Ibn Taymiyyah said, “There are supernatural matters that happen at the shrines to people of Bid‘ah and polytheists like idol worshippers and Christians and deviant Muslims. They think that these matters are from Allah while they are from the devils.”

So, you should seek the Help of Allah and advise those people by pointing out the gravity of their aberration to them. The way to convince them is to state the proofs from Quran and Sunnah that none but Allah The Almighty can harm or benefit. Also, the verses which forbid supplicating anyone besides Allah will be useful in this respect. Fatwas from Islamweb may be a helpful source in this regard; you can reach relevant fatwas via browsing fatwas by subject.

Allah Knows best.