Heresy is the rejection of established beliefs of a religious body, or adherence to "other beliefs." The word "heresy" comes from the Greek word hairesis or choice. The Greek word is a neutral term.
A number of Christian beliefs were declared heresy in the early centuries of the church. Some beliefs declared heresy (Monophysitism, Monothelitism, Nestorianism) are still maintained by Christian churches today, the largest being the Coptic Church. Additionally the Roman Catholic Council of Trent declared Protestantism heresy (a council's rulings that Protestants obviously do not accept).
Arianism-- Jesus less than God -- more than human--
Docetism-- Jesus wholly divine -- his humanity and suffering only seemed to be real--
"Docetist" was first used to identify a particular group in Serapion's condemnation of the Gospel of Peter (c 190 CE). Eusebius reports that Serapion forbade use of the Gospel of Peter on the basis of its docetism.(Eusebius, EH VI.xii).-- from Docetism by A. K. M. Adam (www.evansville.edu/~ecoleweb/articles/docetism.html)
Donatism--personal holiness of individuals validates a church office--
Anyone who apostasized during that time by giving up the Sacred Books, by delivering sacred objects, or betraying other Christians to the government authorities were called a traditor. The Donatist schism began around 311 when a Caecilian, a man who opposed the cult of the martyrs, was irregularly elected bishop of Carthage, after the equally disliked (by the Donatists) Mensurius died. The Donatists argued that Caecilian's ordination was invalid because one of the men who ordained him was a traditor. When Constantine recognized Caecilian, the Donatists appealed. Ultimately, at Constantine's referral, a bishop's council that met in Arles, Gaul (314) rejected the Donatists' argument that a morally unworthy clergyman could not perform valid ecclessial actions. A schism then occurred with the Donatists claiming that they were the only true church. Later Augustine of Hippo (354-430) also spent a great deal of energy fighting Donatism. The schismatic African church remained into the seventh century, when both it and Roman Catholicism were overcome by the Islamic religion.