Mad Swan is the ship between Emma Swan and Jefferson from the Once Upon A Time fandom.
The relationship did not start well. Emma first meets Jefferson when she goes out looking for Mary Margaret. While Emma drives down the road, she swerves to avoid hitting the man, who later introduces himself as Jefferson. Jefferson asks why she was out late at night, in which she replies that she was looking for a dog. Emma insists that she give Jefferson a ride home as she saw that he was limping. Emma and Jefferson arrive at his large house, and he says he has explains that he has no family. Emma goes in with him, and he gives her a map of the area and some tea. The tea is drugged, and she gets dizzy, so he catches her and puts her on the couch. Before she blacks out, she notices he is not limping anymore.
Emma wakes up bound and gagged, but manages to cut herself free by breaking her teacup and using the shards. She finds no exit and realizes Jefferson has been watching her. She finds him in a room sharpening his scissors. She sneaks to hide in the nearest room, where she is shocked to find Mary Margaret who has also been bound and gagged.
Emma starts to free Mary Margaret who explains why she is there, how Jefferson jumped her in the woods. She explains about finding the key to the jail cell as being how she got out. Jefferson finds them and holds them at gunpoint with Emma's gun. He makes Emma tie Mary Margaret back up and gag her, and says that he needs her to do something. Jefferson brings Emma into a room and confronts her with the knowledge that he knows about the curse. He has been trapped here for 28 years doing the same things every day, but remembering the Enchanted Forest and that this is not his life. He tells her that he knows she is special and that she has magic. He tells her he wants her to get "it" to work, and she notices a hat placed on the table.
Jefferson wants Emma to make a hat, since none of the ones he has made have worked. As his hat is a portal jumper than can jump to other worlds. Emma believes he is crazy but appears sympathetic. Emma accuses him of thinking that he is Mad Hatter. She says that he is insane for believing that magic is real and that she can use it. He questions her belief on what is a real world, and he tells her that she and Mary Margaret are not leaving, until she gets a hat to work, so that he can use it to go home.
Emma says that she cannot make Jefferson's hat. Frustrated, he tells her to look through a telescope, where she watches a girl named Paige eating dinner with another couple. He says that she is his daughter Grace, and he remembers their life together, but she does not. He has to watch her with her "new parents", but he will not curse her as he is cursed by telling her who he is. Emma says that she realizes that he just wants to take his daughter back home, and she sympathizes with him. She pretends to believe what Jefferson is saying and admits that he is right about her needing to believe more. Emma waits until he turns away and then grabs the telescope and hits Jefferson with it. She goes to free Mary Margaret, but Jefferson catches her. A struggle ensues, during which Emma notices a scar going around Jefferson's neck. Mary Margaret saves Emma by whacking Jefferson with a croquet mallet and kicking him out of a window.
Emma visits Henry before, when Paige walks by. When she sees her and examines the storybook Henry happily loans her, Emma discovers that Jefferson was telling the truth, for inside is a picture of Jefferson and Grace.
In this episode, he strikes a deal with Regina to get rid of Emma by retrieving something from the Enchanted Forest in exchange for making Jefferson forget his life in the Enchanted Forest, and create a new life for himself and his daughter, Grace. It is assumed that Jefferson cared more about his daughter than Emma.