There aren't a lot of interactions between the two due to Teruteru dying early, but we do know Teruteru was planning on killing Nagito.
Nagito purposefully let Teruteru know about his plan to kill someone at the party they were attending. This caused Teruteru to panic and he devised his own plan to kill Nagito. Teruteru went under the floorboards while there was a blackout and tried to kill Nagito with an iron skewer. His plan almost works, but the Ultimate Imposter pushes Nagito out of the way dies instead. After coming back up from beneath the floorboards, Teruteru is surprised by Nagito's survival and even gets mad at it.
In Episode 4 of Despair Arc of Danganronpa 3: The End of Hope's Peak Academy, Nagito asks Teruteru for a favor. Knowing from Episode 2 that Teruteru keeps in contact with the Ultimate Pharmacist, Komaeda offered him a rare picture of Sayaka Maizono's album in exchange for getting him to meet Seiko Kimura. In Episode 8, Teruteru offers Kazuichi Soda to carry Nagito on his back, as the latter is "within his strike zone."
Komateru isn't very popular due to the little interactions. It's overshadowed by the two boys' ships with Hajime Hinata, Komahina and Teruhina, as well as Komanami and Terunidai. It's also not popular because of Komateru almost being a killer-victim ship if Teruteru's plan worked. Despite these factors, Komateru has it's shippers. It currently has 16+ works on AO3.
This ship is quite disliked in the Danganronpa fandom, it usually shipped with Ultimate Imposter because of trial 1, as Teruteru killed Ultimate Imposter by mistake and was planning to kill Nagito instead, due to this people choose not ship it, as there is barely fanart made showing the pair.
The ship name "Attractive Chef" comes from Nagito being considered "attractive" by the Danganronpa fandom and is mostly liked for his looks, Chef comes from Teruteru being the Ultimate Cook, but he likes calling himself the ultimate chef, another ship name for the two is "Lucky Soup", it comes from Nagito's talent, and how Teruteru can prepare dishes like soup, "Sexy Soup" comes from Nagito being considered "attractive", and how Teruteru can prepare dishes like soup.
- Teruteru's relationship with Nagito on Danganronpa Wiki
- Nagito's relationship with Teruteru on Danganronpa Wiki