Thank you for the question on pseudepigrapha, “What is pseudepigrapha in biblical terminology?”
The word, pseudepigrapha, means “false writing”.” It is writing that is attributed to the Apostles but is consider spurious by the early Church Fathers.
It is admitted that there were many accounts of the life of Jesus. Dr. Luke in writing his letter to Theophilus in Luke 1 states that others have taken written of what they remember of Jesus’ words. His account is an orderly one from beginning to Jesus’ ascension. The Book of Acts is a continuation of the followers of Jesus or the Apostle’s letters to churches or to individuals.
Dr. Luke says this in Luke 1, “Many have undertaken to draw up an account of the things that have been fulfilled among us, just as they were handed down to us by those who were from the the first were eyewitnesses and servants of the word” (Lk. 1:1–2). One can read the list of Pseudipigrapha on the internet and their contents.
As the persecution ended for Christians around 325 CE, churches in various parts of the Christendom held various beliefs, practices, and even readings of religious materials in their worship service. The Book of Barnabas was one of the books that was read in the early churches but was not considered canonical by the early churches. The Didache was one of the teaching manuals for the early Christian church.
SUMMARY: The assigning of certain New Testaments books due to their inconsistent writing as well as the attributed authorship to one of the Apostles as being spurious in light of the Gospels and accepted letters by the early church. Those books are called Pseudepigrapha.
-Kingston