Blood tests can not prove paternity, at best they can exclude it in some cases. Anyway, that's a rather contrived intrigue just to keep the girl datable...This feels like the unraveling of a prequal harem manga with the dad as the MC.
I had a theory that Yuzu's mom was planning to elope with someone else who's Yuzu's biological dad while pregnant with Yuzu but they died before they could make that happen so their dad choose Yuzu's mom and claim Yuzu's their child so she wouldn't have to care for her on her own. I'm sticking to this theory for now since it explains why he suddenly abandoned his fiancee but it looks like Naoomi's family side wasn't the only one who was burdened by this. As far as I can tell, there is still definitive no proof of blood relation. No one has taken a blood test and the people in the best position to tell are either dead or keeping their mouth shut.