Paladins hunt all fiends.
Hellknights hunt demons sometimes.
Both have their own knighthoods as their organizations.
Is there an organization of witch-hunters or hunters of supernatural beings, demons, etc...?!
The Blackravens of the Lands of the Linnorm Kings hunt the White Witches of Irrisen along with their minions in an effort to protect their border.
The Riftwardens are sort of like what you're looking for. They're an organization dedicated to shutting down portals to malign parts of the Great Beyond, fighting planar evils that have intruded into Golarion and most of all, oppose the Blackfire Adepts: a secret society that seeks foul portals burned into reality by the ebon flame and spelunk around in forbidden parts of the cosmos revealed by these ulcerous wounds in the material plane, looking for secret lore and power.
It's said the Riftwardens decend from natives of the Great Beyond who followed the Blackfire Adepts back to Golarion to stop them. After showing up, they began recruiting mortals to bolster the ranks.
Like any really fun inquisitorial group though, while their goals are to oppose evil and save the world, their methods are often ruthless, brutal, merciless and immoral.
They could do nicely. Info on them is in the Pathfinder Chronicles: Campaign Setting on pg. 199 under Lesser Groups.
Any church that has inquisitors would be an organization of witch hunters