Mibu no Tsugai

Sousuke Okita of the Okita family was treated badly for being born as the only omega in the family. After overdosing on heat suppressants, he lost consciousness and time-slipped to the late Edo period! There, he met the Vice Commander of the Shinsengumi, Toshizou Hijikata, and was brought to the detention center as "Souji Okita." Having no other option but to live with the Shinsengumi, Sousuke gradually becomes attracted to Hijikata. Meanwhile, Hijikata continues to mistake Sousuke for Souji Okita.

(Source: Ichijinsha, translated)