Is it permissible to treat a sick person by writing "Bismillah Al-Rahman Al-Rahim" (In the name of Allah, the Most Gracious, the Most Merciful) on their body while also giving charity, even though this method was not mentioned in the Sunnah?

Treating patients whose illnesses medicine has failed to cure could be either a karamah (a miraculous favor from Allah) or an istidraj (a gradual drawing-away, a trial). The determining factor lies in steadfastness upon Allah's commands, avoidance of His prohibitions, and adherence to His Prophet's Sunnah. There is no harm in seeking treatment from a righteous person who treats with methods free from shirk (polytheism), even if their method of treatment is not mentioned in the Sunnah, due to the Prophet’s (peace be upon him) saying: "There is no harm in ruqyah (incantations/exorcism) as long as it does not involve shirk." There is also no harm in the healer touching the patient’s body if their treatment is free from shirk, for Allah has not sent down any disease except that He has also sent down its cure.