What is the origin of some worshippers blowing into their clothes after finishing the prayer and supplication, and was this reported from the Salaf or is there any indication of it in a hadith or narration?

What is prescribed for a Muslim after prayer is to recite the established remembrances (adhkar), and then he may supplicate with whatever he wishes.

Blowing or spitting on the body while reciting something from the Qur'an is a legitimate ruqyah (incantation) that wards off evil or removes it. It is authentically reported that the Prophet, peace and blessings be upon him, used to blow into his hands and wipe his body with them while reciting the Mu'awwidhat (Surahs Al-Falaq and An-Nas). Sheikh Ibn Baz also stated the permissibility of treating magic with the Qur'an through blowing.

If blowing on the body after reciting Ayatul Kursi and the Mu'awwidhat is done with the intention of ruqyah, it is permissible in principle. However, habitually performing this act after the post-prayer adhkar makes it an innovation (bid'ah), unless it is done occasionally or for a specific reason such as illness or obsessive thoughts. The best guidance is the guidance of Muhammad, peace and blessings be upon him, and the worst of matters are their innovations.