Thirteen Knights of the Roman Catholic Church

According to Stiyl Magnus, the knights were created by the Roman Catholic Church after getting the idea from the Knights of England. Their primary purpose appears to be hunting down and eliminating threats and rogue magicians, like Aureolus Izzard

Deep Blood Arc
The knights were sent to take care of Izzard after he was discovered in Misawa Cram school. They were allowed to enter Academy City by General Superintendant Aleister, though their entrance wasn't told to Stiyl Magnus and he found out when he saw a knight's corpse.

The initial strike did not go well, as at least one member was killed, as his corpse was found by Touma and Stiyl. The next night, the remaining members tried to destroy the building Izzard was by marking the Misawa Cram School so the Grigorio Chant launched at the Vatican can strike at Izzard from afar. However, the spell was bounced back by Izzard using his Ars Magna, destroying the Grigorio Chant.

Abilities
According to Stiyl, while the thirteen knights were based off of the Knights of England, compared to their English counterparts the Roman knights were second-rate amateurs. These knights seem to have the same kind of skills as the Knights of England, focusing on heavy armor while attempting to be skilled in both magic and swordsmanship.

Trivia

 * It's unknown if the knights had the same duties as the Agnese Forces, though it seems likely.