Is hanging a paper on which praises and supplications are written, with the intention that the person receives the reward of the praises every time the wind moves the paper, compatible with the Sunnah or is it an innovation?

The fundamental principle regarding acts of worship (ibadah) is that they are tawqif (must be based on divine text and instruction). Dhikr (remembrance of Allah) is among those acts of worship that are not valid unless they conform to Islamic law (Shari'ah). Therefore, writing down dhikr and placing it in the path of the wind is frivolous and a forbidden innovation (bid'ah). A Muslim must follow the Sunnah of the Prophet, peace and blessings be upon him, in dhikr, supplication (du'a), and all other acts of worship, and avoid innovations. Every innovation is misguidance, and the way out of it is to adhere to what the Prophet, peace and blessings be upon him, and his Companions were upon.