What is the ruling in religion, Sharia, and ethics on killing cats that are searching for food, even if they enter homes to find it? And what is the punishment for one who does so?

It is forbidden to kill cats or other non-harmful animals without a legitimate reason, based on the Prophet's (peace be upon him) saying: "No human kills a sparrow or anything larger than it without its right except that Allah, the Mighty and Majestic, will question him about it." However, if a cat causes harm, it is permissible to kill it according to the hadith: "There should be neither harm nor reciprocating harm," provided that there is no other means to دفع its harm except by killing. The killing must be done by a swift method that does not involve torture, as the Prophet (peace be upon him) said: "Indeed, Allah has prescribed excellence in all things. So if you kill, kill well."