Is accidentally running over a cat, and then running over it again to end its suffering, considered a sin that necessitates expiation?

If you accidentally run over a cat, there is no sin upon you, for Allah Almighty says: (And there is no blame upon you for that in which you have erred). As for euthanasia for an animal, scholars have differed on it: some, like the Shafi'is and Hanbalis, prohibited it, while others, like the Malikis, permitted it. The Malikis allowed the ritual slaughter (dhakāt) of animals whose meat is not eaten if there is no hope for their recovery due to illness or blindness, in order to relieve them. The most merciful methods and those furthest from torture must be chosen for euthanasia. As for intentionally running over the cat again to kill it, that was a mistake, and it would have been better to leave it alone if a merciful method was not available.