לע"נ הרב החסיד ר' ישראל צבי בן הרה"ח ר' צדוק
If a man married a half Shifcha half Bas Chorin and they have a child, half the child belongs to him. Half the child belongs to the Shifcha side of the woman because when a Jew has a child with a Shifcha the child follows the mother and doesn't relate to his father. The other half of the child belongs to the father [as well] because it relates to the Bas Chorin side of his mother.
So here we have a case where one essentially has half a child. Asked the Minchas Chinuch [Mitzva Aleph], is he yotzei the mitzva of Pirya Va-rivya?
Rov Genechovski ztz"l answered that we apparently see from Tosfos [Bava Basra 13] that it is a mitzva. The gemara says that if one is half an Eved, half Ben Chorin, we must free him in order that he fulfill the mitzva of Pru U'rivu. Asked Tosfos, why don't we allow him to marry a Bas Chorin and even though she will be doing the aveira of marrying an Eved [לא תהיה קדשה], let us say עשה דוחה לא תעשה and the mitzva of Pru U'rivu will override the aveira?
We see from Tosfos' question that when half a Ben Chorin has a child, even though he is only a half, the mitzva is fulfilled. So too let us say that having half a child [a Ben Chorin marrying half a shifcha] is also a mitzva!!
The Rov ztz"l rejected this and said that maybe there is a difference between half a person having a complete child which is a mitzva and a whole person having half a child which is not.