The Jews did not stop writing during the period of the Old Testament and the New Testament. Many literary works were produced during the time frame between the two testaments. Those works fall into two canonical categories: apocrypha and pseudepigrapha.
They did not attain canonical status, but some of them were cited by early Christians almost on the level with the Old Testament writings, and a few were copied into biblical manuscripts.
Apocrypha means "things that are hidden," and apply to a collection of fifteen books written between approximately 200 B.C. and 100 A.D.
OLD TESTAMENT APOCRYPHAL WORKS: Although never part of the Hebrew Scriptures, all but 2 Esdras appeared in the Greek translation of the Septuagint (Old Testament). (NOTE: Jesus never quoted from the Apocryphal writings --- and the Apocryphal writings were never a part of the Hebrew Scriptures).
They were made part of the official Latin Bible, the Vulgate; all except 1 and 2 Esdras and the Prayer of Mannasseh are considered canonical by the Roman Catholic Church.
The Apocryphal writings represent various types of literature: historical, romance, wisdom, devotional, and apocalyptic.
[First Esdras] is a historical book from the early first century A.D. It parallels material found in the last chapters of 2 Chronicals, Ezra, and Nehemiah. In a number of places it differs from the Old Testament account.
[1 Macabees] is the most important historical writing in the Apocryphal works. It is the primary source of history of the period it covers --- 180 to 134 B.C. The emphasis is God worked through Mattathias and his sons to bring deliverance.
[2 Macabees] also gives the history of the early part of the revolt against the Seleucids; it covers the period of approximately 180 to 161 B.C. 2 Macabees is based on five volumes written by Jason of Cyrene about which volumes nothing is known. 2 Macabees was written shortly after 100 B.C., and is not considered to be historically as accurate as 1 Macabees; in certain places the two books disagree.
[Tobit] is a romance story written about 200 B.C. It is more concerned to teach lessons than to record history. Tobit introduces the concept of a 'guardian angel.'
[Judith] covers the period of 250 to 150 B.C., and covers the topic of obedience to the law, and the 'end justifies the means'. The book contains many historical inaccuracies.
[additions to the book of Esther] to give a more religious meaning to the book of Esther.
[The Song of Three Young Men] is one of three additions to the book of Daniel. It follows Daniel 3:23 in the Greek text.
[Susanna], the story, is added at the close of the book of Daniel in the Septuagint. It tells of two judges who were overpowered by the beauty of Susanna and sought to become intimate with her.
[Bel and the Dragon] was the third addition to Daniel, placed before Susanna in the Septuagint. This story deals with idol and dragon worship.
[Wisdom of Solomon] (which was not written by Solomon) was probably written around 100 B.C. in Egypt. It deals with the pros of wisdom over wickedness. This apocryphal work presents the Greek concept of immortality rather than the biblical teaching of the resurrection.
[Wisdom of Jesus the Son of Sirach] (also known as Ecclesiasticus) emphasizes the importance of obedience to the law --- wisdom is identified with the law; it was written approximately 180 B.C.
[Baruch] in the first section claims to give a history of the period of Jeremiah and Baruch, but it differs from the Old Testament account. The second section is poetry and praise of wisdom. The third and final section equates wisdom with the law. This work was written around 100 B.C.
[Letter of Jeremiah] is often added to Baruch as chapter six, and strongly condemns idolatry.
[Prayer of Manasseh] is a devotional writing claiming to be the payer of the repentant king whom the Old Testament portrayed as being very evil (2 Kings 21:10-17). 2 Kings makes no suggestion that Manasseh repented; though 2 Chronicles 33:11-13, 18-19 state he did repent and God accepted him.
[2 Esdras] was written too late to be included in the Septuagint. Chapters 1-2 and 15-16 are Christian writings; while chapters 3-14 (the significant part of the book) are from about 20 B.C. These writings are mostly apocalypse (prophetic). One of the visions, an obvious error, pictures the Messiah remaining on Earth for four hundred years before dying. Three other false visions stress God's coming intervention and salvation of his people through the pre-existent Messiah. The final section states the end will be soon.
NEW TESTAMENT APOCYRPHICAL WORKS:
[Protoevangelium of James] seems to have been written to glorify Mary. It includes the miraculous birth of Mary, her presentation in the Temple, her espousal to Joseph (an old man with children), and the miraculous birth of Jesus. This second-century work was extremely popular, and undoubtedly had a very major influence on the later views of Mary.
[Infancy Gospel of Thomas] depicts Jesus in a crude manner as a wonder boy, using his miraculous powers as a matter of personal convenience.
Many other infancy gospels were written as the legends expanded; those are as follows: Arabic Gospel of Infancy, Armenian Gospel of the Infancy, Gospel of Pseudo-Matthew, the Latin Infancy Gospel, the Life of John According to Serapion, the Gospel of the Birth of Mary, the Assumption of the Virgin, and the History of Joseph the Carpenter.
Passion Gospels, another class of Apocryphal gospel, are concerned with supplementing the canonical accounts by describing events surrounding the crucifixion and resurrection of Jesus. Those works are as follows: Gospel of Peter, Gospel of Nicodemus (sometimes called 'Acts of Pilate'), and the Book of the Resurrection of Christ by Bartholomew the Apostle.
Jewish-Christian Gospels are works that originated among Jewish-Christian Groups. They include the Gospel of the Ebionites, the Gospel of Hebrews, and the Gospel of the Nazarenes.
Gnostic Apocryphal Gospels include the following books: Gospel of Truth (no reference to Jesus), Gospel of the Twelve Apostles, Gospel of Philip, Gospel of Thomas (no relation to the infancy Gospel of Thomas), Gospel of Matthew (no relation to the canonical Gospel of Matthew), Gospel of Judas, and the Gospel of Barholomew.
Other gospels in this class include those under the names of Holy Women (for example, the Questions of Mary and the Gospel According to Mary), and those attributed to a chief heretic such as Cerinthus, Basilides, and Marcion.
There are also he Apocryphal acts which constitute a large number of legendary accounts of the journeys and heroics of the New Testament apostles --- Leucian Acts, Acts of John, Acts of Andrew, Acts of Paul, Acts of Peter (this apocryphal work teaches Peter was crucified upside down), Acts of Thomas.
Other later apocryphal acts include: the Apostolic History of Abdias, the Fragmentary Story of Andrew, Acents of James, the Martyrdom of Matthew, the Preaching of Peter, Salvonic Acts of Peter, the Passion of Paul, Passion of Peter and Paul, Acts of Andrew and Matthias, Acts of Andrew and Paul, Acts of Paul and Thecla, Acts of Barnabas, Acts of James the Great, Acts of Peter and Andrew, Acts of Peter and Paul, Acts of Philip, and Acts of Thaddaeus.
We also have the apocryphal epistles (or letters) --- The Epistle of the Apostles, Third Epistle of the Corinthians, the Latin Epistle to the Laodiceans, Correspondence of Christ and Abgar, the Epistle to the Alexandarians, the Epistle of Titus, the Epistle of Peter to James, the Epistle of Peter to Philip, and the Epistle of Mary to Ignatius.
There are also prophetic New Testament apocryphal works; those are as follows: Apocalypse of Peter (deals with terror suffered by those in hell), the Apocalypse of Paul, the Apocalypse of James, the Apocalypse of Stephen, the Apocalypse of Thomas, and the Apocalypse of the Virgin Mary.
Other New Testament era apocryphal works include the Agrapha (a collection of sayings attributed to Jesus), the Preaching of Peter, the Clementine of Homilies and Recognitions, the Apocryphon of John, the Apocryphon of James, and certain Gnostic writings such as the Pistis Sophia, the Wisdom of Jesus, and the Books of Jeu.
WHY IS THE APOCRYPHAL WORKS NOT CANONICAL?
Unger's Bible Dictionary gives the reason for the exclusion of these writings: "They abound in historical and geographical inaccuracies and anachronisms." "They teach doctrines which are false or foster practices which are at variance with inspired Scripture." "They resort to literary types and display an artificiality of subject matter and styling out of keeping with inspired Scripture." "They lack the distinctive elements which give genuine Scripture their divine character, such as prophetic power and poetic and religious feeling."
Many of the apocryphal works contains historic inaccuracies as well as contradicting scripture found in the canonical Old and New Testament.
HISTORICAL TESTIMONY OF THEIR EXCLUSION
Geisler and Nix give a succession of ten testimonies of antiquity against accepting the Apocrypha:
1. Philo, Alexandrian Jewish philosopher (20 B.C.- A.D. 40), quoted the Old Testament prolifically and even recognized the threefold division (the Law, the Prophets, and the Writings), but he never quoted from the Apocrypha as inspired.
2. Josephus (A.D. 30 - 100), Jewish historian, explicitly excludes the Apocrypha, numbering the books of the Old Testament as 22. Neither does he quote these books as Scripture.
3. Jesus and the New Testament writers never once quote the Apocrypha although there are hundreds of quotes and references to almost all of the canonical books of the Old Testament. (Exception is Jude 1:14)
4. The Jewish scholars of Jamnia (A.D. 90) did not recognize the Apocrypha.
5. No canon or council of the Christian church for the first four centuries recognized the Apocrypha as inspired.
6. Many of the great fathers of the early church spoke out against the Apocrypha, for example, Origen, Cyril of Jerusalem, and Athanasius.
7. Jerome (340 - 420), the great scholar and translator of the Vulgate, rejected the Apocrypha as part of the canon. He disputed across the Mediterranean with Augustine on this issue; he first refused to even translate the Apocryphal books into Latin, but later he made a hurried translation of a few of them. Only after his death were the remaining Apocryphal books brought into the Latin Vulgate.
8. Many Roman Catholic scholars through the reformation period rejected the Apocrypha.
9. Luther and the Reformers rejected the canonicity of the Apocrypha.
10. Not until A.D. 1546, in a polemical action at the Counter Reformation Council of Trent, did the Apocryphal books receive full canonical status by the Roman Catholic Church.
Sources: Holman Bible Dictionary
Unger's Bible Dictionary
The Best of Josh McDowell: A Ready Defense
The Bible (KJV & NIV)