Its not explicitly but im pretty sure it was implied that the dad is the yakuza. Rememvmber that before dating the uke, she was sad drunk because the man she loved rejected her even though she had slept with him. (That would be when she got pregnant).
And then we learn it was the yakuza that she loved. And the yakuza wanted to take the child and her not wanting a dna test because none of the 2 were the dad.
But what i find odd is we didnt get a single clue as to when and in what circumstances she actually started dating the yakuza.... and at what point did the yakuza knew he was the dad? And how come he didnt even try to take his child....