MGS2: An Illuminati organization that controls the US and the world, led by 12 mysterious individuals. They have created an AI for the purpose of controlling the Internet and the AI considers The Patriots true form and power to actually be American ideals in the minds of the populace. It turns out that one of them aided Philanthropy, yet all 12 of them died over 100 years ago and have a connection to Manhattan.
MGS3: There was actually an organization called The Philosophers who were all just really rich and powerful old dudes in America, the Soviet Union, and China right after World War I who really wanted to kill bad guys with cool expensive guns so they set up a Gofundme for cool gun stuff. The organization all split up after WWII and their money got lost. Eventually they all died or got replaced by The Patriots in America during the Cold War.
MGS4: The Patriots were actually Big Boss and Big Boss's friends (including the woman who cloned the Snakes and experimented on Gray Fox and the Genome Soldiers, a young DARPA Chief, Solid and Liquid's mom, and Ocelot) who got all The Philosopher's moolah and replaced them. Big Boss's commanding officer is their leader. They exist because they were all really sad about The Boss. All the stuff about them dying 100 years before MGS2 was a ruse about the founders of The Philosophers which is a bit of fuzzy math since it's more like 70-80 years and that's if we're only talking founding members but okay. They all split up because of drama bombs and Ocelot was actually on Big Boss's side and the AIs (the one in MGS2 was actually only just one) have actually been running the world and communications for some undetermined amount of time.
PW/GZ/MGSV: Zero actually created an organization called Cipher because it was some hilarious wordplay about his name or something and they used an AI after Otacon's mom made an AI based on The Boss that was installed in the first ever Metal Gear. The AIs were named The Patriots after the DARPA Chief effectively took over because Zero was infected with throat bugs by a guy named Skull Face (his face looks like a skull).