None of those who have attempted to resolve the biblical witness to the Trinity have been able to do so satisfactorily. The Bible teaches that:
God is three Persons.
Each Person is fully God.
There is one God.
If somebody denies any of these three statements about the Father, Son, and Spirit, what he or she is proposing is not true to the teaching of Scripture.
Five teachings gained some prominence in the early centuries A.D., but church leaders rejected them as unbiblical.
Modalism claims that there is one Person Who appears to us in three different forms (modes): sometimes as Father and other times as Son or Spirit. This denies that God is three Persons and fails to account for reports of the Father, Son, and Spirit each being active in different ways at the same time (e.g., at Jesus’ baptism [Matt 3:16-17]).
Arianism claims that there is one God, but denies that the Son is truly God. Arius saw the Son as "similar to the Father,” not of one essence with the Father. He taught that the Son was created by God before any other creature as the one through whom all other creation came into being. He acknowledged him as the greatest created being, but only as a created being. For Arius, the Son was only "god" in the lesser sense that he was made like God.
Subordinationism accepted the biblical witness that the Son was divine and eternal, not created. However, this teaching considered that the Son was not equal to the Father in being or in attributes, but inferior.
Adoptionism taught that Jesus was an ordinary man until his baptism, but then God adopted him as His son and endowed him with supernatural powers. This view denied that Jesus was eternal or that He ever actually became divine. He never became more than an exalted man, whom God called His “Son” in a unique sense.
Tritheism affirms the distinctiveness of the three Persons, but concludes that there are three Gods.
(Spotlight 9, Lesson 3 in Doctrine 101: Learning about God)