The Apostolic Fathers were the early leaders of the Church from the second century to the fourth century CE. Their writings demonstrate a clear understanding of the Trinity of God as taught in the New Testament. Below are some examples:
Saint Ignatius of Antioch
Early reference to the Trinity was mentioned in the Epistle of Saint Ignatius of Antioch to the Magnesians, written around 108 CE. He exhorted believers to live in obedience to “Christ, and to the Father, and to the Spirit” (Ignatius’s Letter to the Magnesians, Chapter 8)
The Didache, or the teachings of the twelve Apostles, dated late first century, directs Christians to “baptize in the name of the Father and of the Son and of the Holy Spirit”.
Saint Clement of Rome (c. 35-99)
Saint Clement of Rome mentioned the Trinity in his writings as well. He rhetorically asks in his epistle as to why corruption exists among some in the Christian community; “Do we not have one God, and one Christ, and one gracious Spirit that has been poured out upon us, and one calling in Christ?” (1 Clement 46:6).
The first apology Justin martyr (100-165 AD)
In chapter 61 on Christian Baptism from Justin’s first apology, he mentioned “the Father and Lord of the universe, and of our Savior Jesus Christ, and of the Holy Spirit” starting with the trinity doctrine in a second century writing.
Justin Martyr is the first to use much of the terminology that would later become widespread in codified Trinitarian theology. For example, he describes that the Son and Father are the same “being” (ousia) and yet are also distinct faces (prosopa), anticipating the three persons (hypostases) that come with Tertullian and later authors.