Schaff, Philip. History of the Christian Church (The Complete Eight Volumes in One). Amazon Kindle Edition, 2014.
Volume 2, Ante-Nicene Christianity A.D. 100-325, “Chapter 4. Organization and Discipline of the Church” Loc. 13792-14769 (part 13).
§58. Church Schisms.
Schisms, or divisions within the Church, are an important issue. When the Church needs to clarify doctrine or practice, it has almost always been as a corrective measure. Schaff discusses four schisms in the third century, all related to restoration of lapsed Christians.
In Rome, a schism was centered around the work of Hippolytus and Callistus, his rival (Schaff 2014, Loc. 14705). Hippolytus advocated strict discipline. He accused Callistus of lax practices as well as a view that God the Father suffered in the crucifixion (patripassianism). A schism was caused, which was reconciled by 235. Hippolytus, even by twenty years later, was recognized as a bishop without negative comment (Schaff 2014, Loc. 14712).
In Carthage, about 250, we find a schism of Felicissimus (Schaff 2014, Loc. 14719). In this situation, the bishop Cyprian, elevated soon after his baptism, was opposed by a presbyter who ordained people himself. The two groups acted independently. After a time of persecution, the opposition party restored the lapsed, but the party of Cyprian did not (Schaff 2014, Loc. 14726). “The church of Novatus and Felicissimus was a resort of all the careless lapsi” (Schaff 2014, Loc. 14733, italics mine). Cyprian gradually moved in the direction of restoration as well.
Rome saw another schism, known as the Novatian schism (Schaff 2014, Loc. 14740). In this situation, the Novatianists rejected any church which re-admitted the lapsed. The leader, Novatian of Rome, objected to Cornelius, bishop of Rome after 251 (Schaff 2014, Loc. 14748). Novatian was supported by a group which elevated him to be bishop of Rome. He was then excommunicated by Cornelius. The sect of Novatian did grow and spread to the sixth century (Schaff 2014, Loc. 14755).
A fourth schism, in Egypt, arose around 305. Meletius, a bishop, “rebelled against his metropolitan, Peter of Alexandria” (Schaff 2014, Loc. 14762). Meletius engaged in ordinations and excommunications in the basence of Peter. Peter, in turn, deposed Meletius. The followers of Meletius eventually joined with the Arians.