In short, the writings known as The Apostolic Fathers are the oldest writings outside of the New Testament to be accepted by the Christian Church at large.  (This is in contrast to, and should not be confused with, the Gnostic Gospels which were rejected by the early church.) The Aposolic Fathers is a collection of writings from approximately the end of the Apostolic Period (70AD) through around the latter second century (150-200AD).  The most well known of these writings are probably "The Didache" and Clement I & II.  The likely dating of these writings generally places them closer to the time of the Apostles than to the Council of Nicea (325AD).  If you have never studied the early church, The Apostolic Fathers is a very interesting and enlightening beginning.  Following are some quotes from various books included in The Apostolic Fathers collection.

The following Quotes come from "The Apostolic Fathers: Greek Texts and English Translations of Their Writings" Second Edition.  Lightfoot, Harmer, Holmes, editors & translators. Baker Book House, Grand Rapids, Michigan.
   The Apostolic Fathers : Greek Texts and English Translations Buy this book here from Amazon.com
   Early Christian Writings : The Apostolic Fathers... English Only Buy this book here from Amazon.com

"The apostles received the gospel for us from the Lord Jesus Christ; Jesus the Christ was sent forth from God. So then Christ is from God, and the apostles are from Christ. Both, therefore, came of the will of God in good order.  Having therefore received their orders and being fully assured by the resurrection of our Lord Jesus Christ and full of faith in the Word of God, they went forth with the firm assurance that the Holy Spirit gives, preaching the good news that the kingdom of God was about to come." I Clement 42:1-3)

"Brothers, we ought to think of Jesus Christ, as we do of God, as 'Judge of the living and the dead.'  And we ought not to belittle our salvation, for when we belittle him, we also hope to receive but little. And those who listen as though these are small matters do wrong, and we also do wrong, when we fail to acknowledge from where and by whom and to what place we were called, and how much suffering Jesus Christ endured for our sake." II Clement 1:1-2

"So then, brothers, if we do the will of God our Father we will belong to the first church, the spiritual one, which was created before the sun and moon... So let us choose, therefore, to belong to the church of life, in order that we may be saved." II Clement 14:1

"Ignatius, who is also called Theophorus, to the church at Ephesus in Asia, blessed with greatness through the fullness of God the Father, predestined before the ages for lasting and unchangeable glory forever, united and elect through genuine suffering by the will of the Father and of Jesus Christ our God, a church most worthy of blessing: heartiest greetings in Jesus Christ and in blameless joy.  I welcome in God your well-beloved name which you possess by reason of your righteous nature, which is characterized by faith in and love of Christ Jesus our Savior.  Being as you are imitators of God, once you took on new life through the blood of God you completed perfectly the task so natural to you." Ignatius to the Ephesians Intro and 1:1 (This is a long quote, but is especially important to any discussion of the Deity of Christ or the Trinity as Jesus is referred to as "our God" and the later reference to the "blood of God".)