Madison does not appear in Act 1 however he is mentioned by Aaron Burr as one of three people responsible for writing the Federalist Papers alongside Hamilton himself as well as John Jay. Madison wrote 29 of the essays, with only Hamilton writing more than him with 59. When Hamilton later begins trying to set up a new national bank, Madison is extremely opposed to the idea, and as such requests the help of his best friend Thomas Jefferson who at the time was in France.
When Jefferson returned to America and was invited by George Washington to become the secretary of the state, he met with James Madison in New York, the latter expecting his arrival, and explaining to him the details of Hamilton's financial plan and asking for his help. After a debate with Jefferson, Madison reminds Jefferson, Washington and Hamilton himself that the latter doesn't have the votes to support his new plan, allowing he and Jefferson to leave in triumph. Washington then tells Hamilton to try and find a compromise with the two.
Although stubborn and still refusing to actually talk to Hamilton, eventually Jefferson convinces Madison to at least hear him out, and talk about possible compromises over dinner, to which Madison accepts. Eventually the three men came to an agreement and the issue was resolved.
Soon after however another political debate arose, thanks to the French revolution. While Jefferson and Madison both agreed to try and help the French Hamilton was against the idea, and ultimately Washington decided to side with the latter, citing that getting involved would be too risky a move for the country at that point. Disappointed Madison later laments alongside Jefferson and Burr about how lucky Hamilton is to have Washington on his side with such a large amount of trust in him. Madison then suggests digging up dirt on Hamilton to the two however and the three begin searching through his financial records, eventually finding irregularities in his funds, and suspicious payments done by a man named James Reynolds.
After Washington steps down from presidency and Hamilton is relieved of his position by John Addams in a fit of fury Hamilton publishes a degrading a humiliating essay about the man, prompting Jefferson, Madison and Burr to confront him and reveal to him what they knew about James Reynolds. Hamilton simply scoffs however, claiming they had no idea what they were even asking him to confess to, before revealing the truth to the three, that he had an affair with one Maria Reynolds and was blackmailed by her husband James into supplying him with funds otherwise he'd expose him. Although disgusted Madison and Jefferson decide to keep this to themselves, while Burr simply tells Hamilton that "rumours only grow".
After Hamilton himself decides to publish "The Reynolds Pamphlet" in a vain attempt to save his reputation, Madison along with Jefferson takes great pleasure in spreading it around to the public, overjoyed at the fact that Hamilton just destroyed his entire political career. Shortly after this Hamilton's son Philip was killed in a duel with a lawyer named George Eacker, and in spite of his dislike for Hamilton Madison showed him great pity for what had happened along with Jefferson.
During the election of 1800, when the only real competition Jefferson had in his goals for presidency was Aaron Burr, Madison suggested they get Hamilton to help him, and although perplexed at the idea, Jefferson conceded that it might actually work.
In the end the votes came to a tie with Hamilton's vote being the deciding one, he picked Jefferson citing the fact that Burr didn't have any real beliefs as his explanation. Madison and Jefferson celebrated their victory, only to be approached by Burr who told him he looked forward to their partnership, Jefferson simply laughed and scolded Burr however, with Madison then commenting how strange it is that the runner up in the elections gets to become vice president. Jefferson agrees and changes this before brushing Burr off, making Madison his vice president instead.
After Jefferson stepped down from presidency, Madison took over from him and eventually himself passed on the torch to Robert Smith. Madison eventually died on the 28th June 1836 at the age of 86 of heart failure.
During the musical's closing number "Who Lives Who Dies Who Tells Your Story" Madison expressed his remorse towards Hamilton's death at the hands of Burr, explaining that he doesn't get enough credit for all that he did for America.
Madison was rather quiet, reserved and soft spoken, however he was also incredibly intelligent to compensate for this and was very knowledgeable in many areas, especially politics. Although at first glance appearing to be slightly more reasonable than Thomas Jefferson, Madison was incredibly stubborn and refused to even talk to Hamilton until the latter convinced him to hear what he had to say. Whenever he was under severe stress, Madison would go into severe coughing episodes.
Madison wasn't by any means a bad person however, as he much like Jefferson he was a man of his word in that he refused to reveal what he knew about the Reynolds affair and only spread it after it had been exposed, also much like Jefferson he did show compassion for Hamilton after his son Philip's death (he is even seen crying after "It's Quiet Uptown" finishes in the movie version), realised that Hamilton could be a good potential ally for he and Jefferson, and even expressed gratitude for Hamilton after the latter's death, respecting him for what he had done for America. Madison was also incredibly close to Thomas Jefferson, with the two being best friends for years before the story's events, going as far as to even become the vice president to the latter.
Madison was a handsome man who had dark skin, short, neatly combed black hair and a muscular build. His clothing was very elegant and formal, with him always wearing a beige suit, paired with a grey frock coat, a white frilled shirt and a cravat, as well as black shoes and white tights.
He also spoke with a very deep and husky voice, and always carried a handkerchief with him due to his chronic coughing episodes.
While personality wise Madison was fairly accurate to his real life counterpart, he physically bears little resemblance to him, with the real half Madison being a very short, skinny man, as opposed to the muscular, tall build he bears in the show. Although he did share the sickly nature and frailty of his real life counterpart.
In real life Thomas Jefferson and James Madison were indeed best friends, however James Madison was on equal level with him throughout their entire political careers as opposed to being his right hand, he also became the vice president to Jefferson far later than the show depicts, since in real life Jefferson actually did accept Burr being his partner, whereas in the show he rejected him in favour of his friend. Burr only had to step down in real life because he destroyed his political reputation after killing Hamilton, and then again Madison still didn't become vice president, instead simply taking over the role of president after Jefferson stepped down.