On The Discrepancy Which Is Supposed To Exist In The Gospels Respecting The Genealogy of Christ (Ante Nicene Vol.7 P.126)

For whereas in Israel the names of their generations were enumerated either according to
nature or according to law,—according to nature, indeed, by the succession of legitimate offspring, and according to law whenever another raised up children to the name of a brother dying childless; for because no clear hope of resurrection was yet given them, they had a representation of the future promise in a kind of mortal resurrection, with the view of perpetuating the name of one deceased;—whereas, then, of those entered in this genealogy, some succeeded by legitimate descent as son to father, while others begotten in one family were introduced to another in name, mention is therefore made of both—of those who were progenitors in fact, and of those who were so only in name. Thus neither of the evangelists is in error, as the one reckons by nature and the other by law. For the several generations, viz., those descending from Solomon and those from Nathan, were so intermingled by the raising up of children to the childless, and by second marriages, and the raising up of seed, that the same persons are quite justly reckoned to belong at one time to the one, and at another to the other, i.e., to their reputed or to their actual fathers. And hence it is that both these accounts are true, and come down to Joseph, with considerable intricacy indeed, but yet quite accurately.