Persona 4/The Animation
During Yu's second day in Inaba, he witnessed Yosuke accidentally crash his bike and get stuck in a trash can. He helped the boy out of the garbage and the two introduced themselves, becoming fast friends as they were both new to the small town and had few other acquaintances.
As thanks for helping him out of the trash, Yosuke offered to buy Yu steak from Souzai Daigaku, but when Chie tagged along they had to settle for eating at the Junes food court instead so Yosuke could afford it. There the group encountered Saki Konishi, a part-time Junes employee who Yosuke had a crush on. She introduced herself to Yu and tells him to look out for Yosuke.
When Saki was found murdered, Yosuke was left devastated. The boys and Chie had discovered the hidden Shadow World in the TV about a day prior, prompting Yosuke to insist upon investigating the world for clues about Saki's death. He and Yu ventured in and discovered Saki's manifestation of her family's liquor store where she appeared in the world. It was there that they encountered Yosuke's Shadow self, only for Yosuke to reject its accusations of him only trying to solve the mystery because it sounded interesting and everything else was boring to him. That his happy-go-lucky nature was just an act to hide his fear of being alone. The Shadow turned into a giant monster upon rejection and attacked Yu and Yosuke. Since Yu had obtained his Persona at that point, he protected Yosuke from the monster's onslaught, diving on top of him at one point to knock him out of the way of the Shadow's attack.
When Yosuke continues refusing to accept his Shadow's claims as true, Yu punches him in the face to snap him out of his denial. He reassured Yosuke that he really did love Saki and gives him the courage he needs to accept his Shadow. The Shadow Yosuke becomes his Persona, Jiraiya, and the two have Teddie send them back home for the day. Once they return to the real world, Yosuke thanks Yu once more and says he's gonna have a good night's sleep that night thanks to his help. The next day, the two meet on the way to school and resolve to solve the murders and put a stop to them before anyone else dies, forming the Magician Social Link. From that point on, the two share an extremely close bond, with Yosuke taking to calling Yu "partner."
When the Investigation Team attempts to rescue Yukiko from the TV, they encounter Chie's Shadow self along the way. Though it attacks all three of the group, Yu more regularly reacts when Yosuke is in danger. It is when the Shadow starts strangling Yosuke that Yu first triggers his Wild Card ability to save him.
After rescuing Yukiko, the group meets at Junes to discuss what she is able to add to their evidence for the case. Yosuke perks up at the mention of a particularly unusual realization, causing Chie to liken his reaction to spontaneously coming back from the dead. Yu simply replies that Yosuke "looks good for dead." Additionally, whenever a new victim appears on the Midnight Channel, aside from Naoto, Yosuke is the first to call Yu concerning who and what was shown. During the school camping trip, Kanji excitedly compliments Yu's swimsuit, causing Yosuke to appear distinctly upset by the attention he's getting.
During the battle against Mitsuo Kubo's Shadow in the anime, Yu is trapped in the void within the Shadow's outer shell. He is unable to summon any of his Personas, with the core of the Shadow attempting to convince him that his bonds are worth nothing. It is ultimately Yosuke calling out and breaking through the illusion that allows Yu to escape. From that point on, the two refer to each other using their given names rather than their family names, which the other members of the team immediately notice.
Yosuke's suggestion for a Group Date Café is chosen as their homeroom's attraction for the Culture Festival. After the group waits for an unnervingly long time with no one showing up, they are forced to simulate their own group date to attract potential customers. Since there are two more guys in the group than girls, either Yu or Yosuke is forced to sit on the girls' side. If Yu sits on the boys' side, he can ask Yosuke which of the guys he likes best. Yosuke answers that he thinks Yu would be most reliable before realizing he's playing along and snaps at Yu. If Yu chooses to sit on the girls' side, he is asked which of the guys he would date. If he chooses Yosuke, in spite of his initial unease toward the insinuation, the player notices he looks somewhat proud of Yu's response.
In the anime, Yu chooses to sit on the girls' side of the table. Yosuke asks the same question about which of the guys they would date. Yu responds by gazing dreamily at Yosuke, causing the fawn-haired boy to become extremely flustered. When Yukiko asks what's wrong, he blurts out that he doesn't know what happened, but his mind went somewhere he could never come back from. When Yu asks if it's his girl voice that's bothering him, Yosuke freaks out even more and yelps at him to knock it off, bolting over to a nearby shopping bag and frantically searching for a cold drink to clear his head (which, of course, Chie forgot to bring).
After Nanako's "death," Yu tells everyone to go home when they leave the hospital, having decided against taking vengeance on Namatame. Everyone leaves as he instructs, but while he's beginning to choke up at losing her, Yosuke returns to comfort him. Yu casts aside his calm, deadpan facade and begins to bawl to Yosuke, who stands by and gives him an understanding shoulder to cry on.
Once Yu establishes the Magician Social Link with Yosuke, the player can choose to spend free time with him. The events of the Social Link primarily follow Yu and Yosuke casually hanging out around town. Over the course of the events, Yosuke regularly faces people and coworkers stressing him out, mocking him, and asking unreasonable things from him due to his dad's job as the Junes branch manager.
At one point, two particularly troublesome part-timers start badmouthing Yosuke by bringing up his former crush on Saki. Yu is given the option to stand up for him by telling the girls to shut up. If this choice is followed, once the girls leave Yosuke thanks Yu for helping him out. He ends up smiling sheepishly and telling him it made him happy to hear Yu say that stuff to them for his sake.
Eventually, Yosuke confides in Yu about his lasting grief over Saki's death. He once again admits to his Shadow's claims of being bored with Inaba and wanting to play the hero, realizing that he was partly jumping at the mystery to forget that Saki was gone. Yu realizes that he has been acting as Yosuke's crutch since the investigation started and Yosuke thanks him for making him realize the issues he was holding within himself. Yosuke begins to cry over his realizations and grief, giving Yu the option to hug him. In spite of calling Yu a dumbass and saying that hugs were for girls, Yosuke accepts the hug anyway as Yu acts as his shoulder to cry on, walking him home when they're done for the day.
In Yosuke's final Social Link event, he confesses that he originally didn't trust Yu out of jealousy. He saw him as the likable hero he wanted so desperately to be, in spite of being proud of him for it as well. He realized he wanted to be acknowledged by Yu the most and asked him to hit him to "knock the crap out of him and become equals." Yu agrees (and just straight-up punches him without warning in the anime) and the two brawl it out for a short time, both ending up on the ground in pain. Yosuke thanks Yu once again and gives him a bandage in case he starts bleeding.
Dummied content from Persona 4 reveals that Yosuke was originally going to be a potential romance route for the player. Yuri Lowenthal even recorded lines for his confession event for the English version of the game, implying that the option was not scrapped until the last minute.
The ship sailed as a result of the strong bromance between the two coupled with the somewhat repressed, yet entirely unsubtle implications of Yosuke having feelings for Yu in the anime. The ship is regularly teased by the source material, particularly in the anime and spin-off games.