hi!! i wrote a long reply to someone after you asking about this!
essentially:
1) Kiku was written as a gay man. the author inadvertently confirmed this outside of the narrative by putting only him and no other charas from the series in a Japanese convention for LGBT representation in manga
( https://twitter.com/KUMOHARU/status/1132975043506462725)
2) omake in volume 10 makes it seem that it was konatsu who was in love with him since she was a teenager. kiku knew and it made him feel disgusted and guilty, and from there he started being really cruel to her on purpose in hopes that she would hate him instead of loving him - but it didn't work.
3) same omake the yakuza guy had been looking out for her as a favour from kiku who felt too grossed out to be around her and saw her as a kid, so i doubt it was him either. it seems to just be a random one night stand, and yakumo asked the boss to not disconfirm it as his child because the shouwa era for women having children out of wedlock was extremely extremely frowned on and she would have been discriminated against by the town!
hope this helps(๑•ㅂ•)و✧
Wahhh thank you soo much. Your reply enlighten myself with this story and really helps. Thanks once again to reply my question (≧∀≦). Wanna talk about kikku personality and the story itself but my english is really broke. I couldnt choose the best word how to describe it.
dont worry about it! im happy i could be helpful!
Soo my stupid head just realize after rewatch and reading the manga that shinsuke father is kikuu/ yakumo ? Za heckk ? My mind just telling me that shin father is the boss yakuza one. Cuz i cant take it :((