What is the ruling on the custom of slaughtering a sheep as a fidyah for someone afflicted due to an accident, passing it over him, throwing some of its meat to the devil, and distributing the rest to neighbors? Is it invalid, or is there no harm in it?

Slaughtering to thank Allah for the recovery of an injured person or for charity on their behalf is permissible if the slaughter is for Allah. It is forbidden if it is for other than Allah, such as slaughtering for devils with the intention of glorifying the one slaughtered for and drawing near to them, as this is polytheism (shirk). As for passing the sheep over the injured person, this is from the acts of sorcerers. As for throwing meat to the jinn, what is prescribed is to give charity to the Muslim jinn by a Muslim eating the meat off the bone, then mentioning Allah's name over it and throwing it with the intention of charity. Throwing it in this manner contains several prohibitions, including wasting food, drawing near to the jinn, and obeying sorcerers.