Yuga seems to interact with her more than with his other classmates. She often teases him about his stomach aches as a result of his Quirk and also managed to beat him with ease during the U.A. Sports Festival. However, she did look apologetic when she saw he was dazed from her punching and knocking him out.
A running gag is her interrupting him when he is arrogantly speaking about himself, often making him mad.
They are classmates and their first meeting was in the Quirk Apprehension Test. When Izuku Midoriya has his Quirk restrained by their teacher, Yuga gives Ochaco comforting words by stating he'll be by her side if Izuku is expelled as she is confused and can't recall his name. 
They are later paired up against Thirteen and their teamwork is a bit rocky. When they were in a bind, Yuga had correctly guessed that Ochaco was thinking of Izuku in their match. He inquired if she had feelings for him, which resulting in her blushing and letting go of the rail she was clinging to. However, this also awakened her combat instincts and allowed her to take down the hero.
Yuga's words caused Ochaco to ponder over her feelings for Izuku and they were shown to stick with her before she realized that he was right about she felt about Izuku.
The two first met at the entrance exams where Yuga saved Izuku from being attacked by a robot, though he did this for points as he remarked that the latter made good bait and he would most likely not see him again. Izuku later excelled in the exams and became classmates with Yuga. It was shown his opinion hadn't changed, as he remarked on Izuku's lack of skill to Ochaco. However, Izuku surprised him with his powerful Quirk which allowed him to remain in the school.
After this, the two had no further interaction that was notable until the Remedial Course Arc. Aoyama would act strangely around Izuku who would note that he could never get a good read off the latter.
Izuku is later scared when Yuga spies on him as he slept and left a message (in cheese) to say he knows Izuku's secret, which left Izuku wondering if Yuga is aware of his secret. In training, Izuku is called out to by Yuga and is shown one of his new moves though it causes him severe stomach problems. Seeing him in this state, Izuku took Yuga away to recuperate before he asks him what he meant in his message.
Yuga explained that he is aware of Izuku not being accustomed to his Quirk and reveals that he went through a similar experience and compared his powers leaking out in his childhood out to Izuku's initial lack of control of his own Quirk before they both overcame it. He then tells Izuku that he is not alone in hardships, as it is better to face them together or they won't excel. His words relieve and cause Izuku to smile and thank him for his support. After a few days, Izuku and Yuga became good friends with some of the class noting on their frequent interaction.