Shinso and Ojiro are barely shown interacting in the anime or manga.
Their only canon interaction is during the Sports Festival Arc, when Shinso uses his mind control quirk to use Ojiro for his cavalry battle team (along with several others). After the cavalry battle is over and Shinso's team moves onto the next event, Ojiro resigns from the festival because he does not feel as like it was fair that he should be allowed to compete in the next event, since he has no memory of participating in the previous event.
Ojiro later warns Deku about Shinso's quirk because he doesn't approve of Shinso's method of winning.
During Shinso and Deku's battle, Shinso insults Ojiro by calling him a "monkey" and saying that he kept "going on about his pride" and "he was dumb for throwing away his chance."
In the manga, during the battles between 1-A and 1-B, Shinso reappears and Ojiro is shown to look irritated by his appearance. They do not officially interact, however.
Though they don't have much interaction in canon, ShinOji seems to have a decent following within the fandom.
Most of their following comes from the idea of Shinso apologizing to Ojiro after the sports festival and eventually becoming friends with him.
With the 1-A & 1-B battle arc involving Shinso in the manga, the idea of them becoming rivals or sparring partners also became a popular idea.
- Their Japanese ship name is "心尾", which roughly translates to "heart tail" in English.