Sonia and Mikan don't interact very much despite being from the same Danganronpa game. Despite this, Sonia and Mikan appear to be on very good terms with each other, and are seen to be good friends.
In Chapter 1, when Mikan was tripping for the second time, Sonia was the first one who suggested helping her up, and later in the Chapter when Mikan chimed in before the others could vote, Sonia was the first one to say that they should hear what Mikan has to say.
In Danganronpa 2: Goodbye Despair, Sonia also invited Mikan to come with the girls swimming.
In the Danganronpa 3 Anime the girls can be seen playing videogames together.
The ship sailed due Mikan's and Sonia's friendly interactions with each other, supporters of the ship, like to image that Sonia would help Mikan with her self-confidence problems. In fanarts Sonia is often seen to comfort Mikan or Mikan and Sonia are doing other couple-like things. In fanfictions, Mikan often falls first in love with Sonia due her kindness, sometimes Sonia even protects Mikan from her bullies. While the ship has a very small fanbase, the ship is generally very well received and seen as very healthy for both characters.
Reason's why the ship is shipped, is because of the, "opposites attract" trope, the trope is fairly popular and Mikan is very timid and cries easily, while Sonia is mostly always positive and nice, so the ship perfectly matches in the trope. Another trope, that matches the ship is the "popular girl x unpopular girl" trope, while Mikan was bullied, Sonia is a princess and so fairly popular among people, so they also perfectly match in this trope, which seems to appeal to some people.
The ship is a rare-pair within the Danganronpa fandom, while being a rare-pair it still got some attention, mostly because Sonia's nice behaivor towards Mikan. Otherwise, the ship is also decently popular among femslash shippers . Nevertheless, the girls have several more popular ship's, that surpass Sonikan's popularity easily, namely, Band Aid and Nanamiki for Mikan and Sondam and Soniaki for Sonia. The ship currently has about 7 fanfictions on AO3.