What distinguishes the writings of the New Testament from all other early Christian writings was their apostolic origins. That is, all writings that were ultimately determined by the ancient church to be apostolic were included in the New Testament. This required the ancient church to make decisions because there were many writings in the first three hundred years making a claim to to have been from the apostles, including those listed below.
Probably because of their claim to apostolicty, the following books achieved what Bruce Metzger has called “temporary and local canonicity.” That is, they never received widespread acknowledgement as apostolic and were ultimately rejected from the New Testament canon.
The Gospel of Peter
The Acts of Paul
The Acts of John
The Acts of Peter
The Epistle of the Apostles
The Third Epistle of Paul to the Corinthians
The Epistle to the Laodiceans
The Correspondence Between Paul and Seneca
The Apocalypse of Peter
The Apocalypse of Paul
Source: Metzger, Bruce M. The Canon of the New Testament: Its Origin, Development, and Significance, Oxford University Press, 1987.