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 5. Christian Worship” (Includes an introduction and sections 59-74).
§74. Heretical Baptism.
“Heretical baptism was, in the third century, the subject of a violent controversy, important also for its bearing on the question of the authority of the Roman see” (Schaff 2014, Loc. 15556). Cyprian and Tertullian rejected baptism which was conducted by heretics. Because the heretics didn’t believe the same doctrines, their use of water was considered ineffective. however, normally the efficacy of the sacrament was seen to be in the Word of God rather than the priest’s holiness (Schaff 2014, Loc. 15565). As a result, many would consider the baptism valid but call the baptized person to be nurtured in the true Christian faith. A wave of persecution in the mid third century largely stopped debate on this issue. However, in the fourth century, the view of Rome, in which the baptism would be recognized and accepted, gradually prevailed (Schaff 2014, Loc. 15587). The consensus by the late Middle Ages was that any baptism performed in the Triune Name was valid (Schaff 2014, Loc. 15594).