Upvote:3
The Catholic Church has no official position on this, since it is of minor importance (albeit an interesting problem).
The consensus of theologians who have studied the problem (Catholic and non-Catholic, who hold the Church’s firm belief in the Virgin Birth and the maleness of Jesus) is that, presumably, the genetic material for Jesus’s paternal complement of DNA was created miraculously.
This is likely to be the case, because the result of a parthenogenesis (viable parthenogenesis is extremely rare, if not nonexistent, in humans) would be a woman, not a man.
Moreover, it is unlikely that any of Mary’s DNA was simply “duplicated” in order to fill out any part Jesus’ paternal complement: generally, when maternal DNA is accidentally duplicated (even when there are no “extra” chromosomes), there are grave birth defects due to a phenomenon called genomic imprinting.
The fact that the Son was conceived as a healthy man would, therefore, be further confirmation of the miraculousness of Jesus’ conception and birth.
(For a decent overview of various positions, see http://archive.sltrib.com/story.php?ref=/lifestyle/ci_3207769. Note that the article represents a diversity of opinions, some of which are not compatible with orthodox belief in the Virgin Birth. Among those cited in the article, David Wilcox and Ronald Cole-Turner uphold the Virgin Birth; Wesley Wildman does not.1)
Some apologists, such as Tim Staples, mentioned by the O.P., would argue that all of the genetic material came from Mary (presumably with some kind of miraculous transformation that would account for the maleness and lack of problems caused by genomic imprinting, although he does not address this issue in the video).
1 Also, the article misrepresents the reason for the dogma of the Immaculate Conception: it has nothing to do with the supposed evilness of male seed—after all, Mary herself was conceived by a normal sexual act—but stems from the belief that Mary, in view of her divine motherhood, is all holy (panagia), and hence is exempt even from the effects of Original Sin.