The series "Impossible Heir" begins with Tae-oh finding himself at a crime scene, holding a weapon, but he doesn’t remmber anything about what happened. Then, the scene shifts to years ago when we see Tae-oh moving to a small town, his mother's old hometown. He finds a place to stay, and that night, from his house, he can see what happens in a nearby mansion. People are partying outside, while a man stays inside, looking out from the window. The next day, Tae-oh goes around looking for a job but gets rejected because he's underage. He meets the guy who looked out of the window the day before and he is stealing some snacks from a convenience store, but the owner doesn't say anything. Tae-oh finally gets a job at a restaurant. When he gets out, he again sees the stealing guy. Tae-oh sees him again outside of a hardware store, but this time, he approaches Tae-oh to brag about why he's stealing. But no one in town does anything because he is Kang In-ha, the illegitimate son of the Kang Oh Group's chairman. However, Tae-oh sees that the people in town just ignore him because all the things he took were worthless, and In-ha just wants attention. In-ha is clearly upset. The next day, Tae-oh is placed in the same class with in ha. The teacher introduces Tae-oh as the one who scored in the top 0.1% nationwide on the university entrance mock test. At lunch, In-ha starts to bully Tae-oh. He doesn't let the other guy sit and throws food at him. But Tae-oh doesn't back down and hits him right back. They end up fighting in the canteen until the teacher arrives and scold them. After the fight, they both have to stay at school to fill out a letter of apology for fighting. The teacher let both of them go, but In-ha's friend comes to tell them the news and lies, saying that only In-ha can leave. In-ha acts cocky about it but later feels ashamed when he learns the truth and drives off.

He returns to his family mansion, where his half-brother in ju is showing off his shooting skills and having fun with his girlfriends. Later, the teacher comes in and tells Tae-oh to go home. As he's leaving, someone calls him, and he rushes to see his mom at a monastery, who is disguised as a monk. It turns out that the person who called him was his stepdad, who had been put in jail for murdering his mom. But now, he knows that Tae-oh's mom is still alive and that they framed him. The stepdad knows where they are and sends people to kill Tae-oh's mom. As his mom is about to leave on a bus, a group of thugs starts to search the area. After that, Tae-oh goes to the boxing club and considers signing up because he wants to be stronger to protect his mom. In-ha happens to be a member of the club and asks if Tae-oh wants to learn boxing to beat him up. Tae-oh ignores his question and walks away, but In-ha tells him that he will teach Tae-oh if he can beat him just once. They get in the ring, and In-ha quickly knocks Tae-oh to the ground. Tae-oh has a flashback of his stepdad and the times he abused him and his mom. All of this anger fuels him, and he gets up and punches In-ha non-stop until he realizes it was just an illusion. Somehow, this fight makes In-ha and Tae-oh become friends. The next day at school, when someone makes fun of Tae-oh for his dad being a murderer, In-ha sticks up for him. While doing so, he compares the social differences between his dad and his friend's dad to insult him. Tae-oh isn't impressed by that and leaves for the rooftop, with In-ha following him. On the rooftop, Tae-oh shares his family secret with In-ha and suggests a plan that could help both of them climb the social ladder to reach the highest level of power.

Years later, Tae-oh and In-ha are in college, ending up at the same university. Tae-oh is working hard at different jobs to support himself including tutoring and warehouse loading, and come back home early in the morning. He now lives in a small apartment across the street from a girl named Hye-won. At home, In-ha hires a private chef and throws a birthday party for Tae-oh, while Tae-oh helps In-ha with his studies. In-ha informs him that he has recommended Tae-oh to be the math tutor for his little sister as a birthday gift. At the university, Tae-oh is called in to receive compliments on his report that outlines future strategies for the Kangho company. The project is based on the Co-prosperity Cooperation Centre, a hub for investing in and acquiring startups, with a main focus on mergers and acquisitions. The professor offers to buy it, but Tae-oh decides to keep it for the future instead. after Tae-oh leaves, the professor still calls someone to talk about the project. That person is Jeong-ju, another half-brother of In-ha. In the library, Tae-oh learns that In-ju and Jeong-ju are competing to be the successor of the Kangho Group and starts thinking of a plan. At that moment, he sees Hye-won, who is also studying in the library. Hye-won approaches him at the vending machine, introduces herself, and tells him to stop ignoring her. In-ha arrives, and they have lunch together. He notices that Tae-oh is interested in Hye-won, but Tae-oh denies it. Later that day, Tae-oh goes to tutor Hee-ju, In-ha's little sister. Hee-ju isn't focused on studying and is more interested in her new tutor instead. That evening, when he returns home, Tae-oh sees Hye-won's mom breaking the door and nagging her daughter for money. He then sees Hye-won sadly walking on the street and follows her with an umbrella when it starts to rain. He asks her to have a beer together, and they have a talk for the first time. The next day, Mr. Kang, the chairman of Kangoh Group, asked his assistant to report on his sons' actions to consider who will become the successor. His second son, Seong-ju, seems to have more potential than his older brother, In-ju, who only cares about partying. Meanwhile, Geom-seok, Mr. Kang's wife and the biological mother of Seong-ju and Hee-ju, is scheming with her son to win the succession game. She gets In-ha to sign away his rights to the company shares; otherwise, he will be cut off from his financial support. But little does she know, it is a part of Tae-oh and In-ha’s plan. Later, In-ha and Tae-oh plan to hang out, but In-ha meets Hye-won and invites her over. They later go to In-ha's house, and In-ha blatantly asks her to date him. She turns him down, saying she's too busy to date. Tae-oh is uneasy with In-ha hitting on his crush but doesn’t say anything. Later, Hye-won and Tae-oh leave together. They are on the bus but sit in two different places. Hye-won texts Tae-oh to ask him to go with her to an old place she lived. She feels they're alike and thinks Tae-oh is using In-ha to get ahead, and she wants to do the same; she asks if Tae-oh would help her.

TL;DR "Impossible Heir" begins with Tae-oh at a crime scene, weapon in hand, with no memory of events. Flashback: Tae-oh moves to his mother's hometown and meets In-ha, the illegitimate son of the Kang Oh Group chairman. In-ha bullies Tae-oh, but they eventually become friends. Tae-oh’s stepdad, wrongfully imprisoned, knows Tae-oh's mom is alive and sends thugs after her. Tae-oh joins a boxing club to protect his mom. He and In-ha plan to climb the social ladder. In college, Tae-oh helps In-ha study and tutors his sister. They form a plan against the scheming family, aiming for the Kangho Group's succession.