As a child, Patrick's parents took him to undergo an illegal procedure called accelerated critical neural pathway formation which dramatically increased his intelligence beyond what Humans would call genius level. However, the procedure also left him with a child-like personality, resulting in him being taken into psychiatric care to live with others like himself.
In 2374, when it was revealed that Doctor Julian Bashir had also undergone the same procedure, Doctor Karen Loews – the psychiatrist in charge of Patrick's case – took him, along with Jack, Lauren, and Sarina Douglas, to Deep Space 9. Dr. Loews believed that meeting someone like them who had managed to fit in to normal society would be helpful to them.
Along with the others, Patrick studied Gul Damar's speech calling for peace talks between the Dominion and the Federation. Together, just by watching the speech, they were able to determine the entire story of Damar's rise to power without ever having heard any of it before. Bashir was very impressed, and encouraged their thirst for knowledge about the Dominion. They asked to watch the holographic recordings of the peace talks, and determined that the Dominion was stalling for time to solve their shortages of ketracel-white. Had the Federation signed the peace treaty, they would have almost certainly lost the war.
Grateful to them, Starfleet provided Patrick and the others with classified reports and war plans. They quickly determined that the Dominion was certain to win the war and that the only way to prevent the loss of billions of lives was to surrender immediately. Unsurprisingly, Captain Benjamin Sisko rejected this immediately. Jack, Patrick, and Lauren attempted to take Starfleet's classified information directly to the Dominion, knocking Bashir out and leaving him in Sarina's custody, so they could win the war more quickly, thus saving lives. Jack miscalculated, however, as Sarina released Bashir who then stopped him from meeting with Weyoun and Damar. Starfleet, however, remained willing to listen to any ideas they had on how to win the war. (DS9: "Statistical Probabilities")
In 2375, Patrick and the others developed a procedure that would cure Sarina of her inability to properly communicate with others. With Patrick posing as a Starfleet admiral, they took her to Deep Space 9 where Bashir was able to perform the procedure successfully. Although possessing little knowledge of Starfleet regulations, Patrick was able to order officers around by answering every question with "That's a stupid question." (DS9: "Chrysalis")
Memorable quotes Edit
"Sounds like the plasma flow's out of sync."
"Better realign it."
"I was thinking that. "
- - Patrick, correctly identifying an engineering problem to Miles O'Brien (DS9: "Statistical Probabilities")
"Patrick! Come on."
"What are you doing here?"
"That's a stupid question."
"Where did you get these uniforms?"
"That's a stupid question, too."
"How much time do we have left?"
"Sixty trillion years, seventy at the most."
"Couldn't you make us normal like you did for Sarina, and then we could all stay together."
Background information Edit
Patrick was played by actor Michael Keenan.
Two costumes worn by Keenan as Patrick were later sold off in the It's A Wrap! sale and auction. The first, a brown zip-up jumpsuit as featured in "Statistical Probabilities" was sold for US$113.00.  The second, a red chenille jumpsuit with textured stripes and belt loops as seen in "Chrysalis", was sold for US$127.50. 
The script for "Statistical Probabilities" describes the character of Patrick as "a child-like man in his fifties [...] He looks scared, lost". This would put his year of birth somewhere between 2315 and 2324. 
The characters of Jack, Patrick, Lauren, and Sarina were collectively referred to as the "Jack-pack" by the Deep Space Nine writing team, with each character having a specific personality trait. In terms of Patrick, actor Michael Keenan found the character quite straightforward. "It was pretty specific." he recalled. "I mean, he's essentially a child, so I just played him that way. Children have instant access to their emotions and they don't filter anything, so that's what I did." (Star Trek: Deep Space Nine Companion, p.514)
Having previously worked on Star Trek: The Next Generation (as Maturin) and Star Trek: Voyager (as Hrothgar), Keenan walked into the role of Patrick. "It was really kind of funny," he laughed, "I'd already done The Next Generation and Voyager so as a joke, I went into [Casting Director] Ron Surma's office and said, 'Hey Ron, I've gotta do the Triple Crown.' Ron laughed, and the very next week he called me in for "Statistical Probabilities"." (Star Trek: Deep Space Nine Companion, p.514)
Though he never auditioned for the musical scene in "Chrysalis", Keenan just gave it his best shot and ultimately enjoyed it. "They didn't audition us for the scene; it was just there. So I thought, 'Well, either we do it right or they dub it later'," he laughed. (Star Trek: Deep Space Nine Companion, p.615)
Patrick appears in the Star Trek: Typhon Pact novel Zero Sum Game along with Jack and Lauren. The three of them are working for Starfleet Intelligence in the year 2382 when they discover several startling revelations about the Breen.
Patrick also has a card in the Star Trek Customizable Card Game, which describes him as an "Idiot Savant".