In the aftermath of the persecutions, controversies arose over the sacraments, which required clarification of the Church's sacramental theology. Out of those controversies, new schisms emerged which had a correct understanding of the doctrine of the Trinity, but incorrect understandings of ecclesiology (the doctrine of the Church) and incorrect understandings of what makes a sacrament valid and effective. The significance of these schisms cannot be overstated, since it is still true to this day that the practice of rebaptism is one of the most prevalent acts of schism against the universal Church, and one of the greatest barriers to unity.
Links
To listen to Mike Aquilina's episode 18 on Cyprian of Carthage: https://www.catholicculture.org/commentary/ep-18-short-happy-life-cyprian-carthage/
To listen to Mike Aquilina's episode 39 (the 2nd of 3) on Augustine of Hippo & the controversies: https://www.catholicculture.org/commentary/39augustine-part-2-mob-made-bishop-makes-his-mark/
To read the anonymous document On Rebaptism: https://www.catholicculture.org/culture/library/fathers/view.cfm?recnum=1729&repos=8&subrepos=0&searchid=2390688
To read St. Augustine's treatise, On Baptism, Against the Donatists: https://www.catholicculture.org/culture/library/fathers/view.cfm?recnum=3294&repos=8&subrepos=0&searchid=2390773
To read St. Augustine's letter, The Correction of the Donatists: https://www.catholicculture.org/culture/library/fathers/view.cfm?recnum=3296&repos=8&subrepos=0&searchid=2390689
For more on the controversy surrounding the third and fourth century schisms and the implications for the Sacraments, see the book:
Reading the Church Fathers: A History of the Early Church and the Development of Doctrine: https://sophiainstitute.com/product/reading-the-church-fathers/
For all the details on Novatian, see the book: Novatian of Rome and the Culmination of Pre-Nicene Orthodoxy: https://wipfandstock.com/9781606087800/novatian-of-rome-and-the-culmination-of-pre-nicene-orthodoxy/
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Join the Original Church Community on Locals: https://theoriginalchurch.locals.com/
Dr. Papandrea's Homepage: http://www.jimpapandrea.com
Theme Music: Gaudeamus (Introit for the Feast of All Saints), sung by Jeff Ostrowski. Courtesy of Corpus Christi Watershed: https://www.ccwatershed.org/