This doctrine exists nowhere in the New Testament. Even the mention of a father, son and holy spirit says nothing at all about a triune God. It makes perfect sense for there to be a father God, a holy man who is his "son" and divine inspiration called the Holy Spirit in Matthew, but it says nothing at all about a Triune God.
Besides, the NT Jesus himself repeatedly refers to "my father" and the difference between himself and his father, not to mention calling on his father on the cross. So it is pretty clear that the original Christian paradigm didn't have this concept at all.
I see that you are Jewish, and since Christianity has its origins in Judaism, maybe a discussion of the commonalities between the two might help.
The concept within Judaism of the
shekinah, even though Judaism never identifies the shekinah as God, the shekinah is often
spoken of as God. That the temple was the "house of God", but that God the Father never entered it, His divine presence, or glory, or Holy Spirit, did. The divine presence of God rested on Mount Sinai as well, that divine presence spoken of as God. So, we have God the Father, as well as
something else often spoken of as God, but not God the Father, acting on behalf of God, and acting
as God.
I don't think I have said anything so far to insult you, or Judaism for that matter, and I hope I don't. But we are now left with, rather than a Trinity, a "di-vinity" of sorts, God the Father and His Holy Spirit. Within Christianity we not only recognize that "di-vinity", but also the concept of the
Logos, or
Word, of God, acting much the same as the shekinah of Judaism. As John wrote,
In the beginning was the Word, and the Word was with God, and the Word was God, ...the Word became flesh and dwelt among us. According to the Christian tradition I suppose he could have written "...the Word, and the shekinah, and they were God".
So in the end, that idea of a Trinity does appear in the New Testament. It is where the Church Fathers originally got the idea from.