Where and When Did The False Doctrine of Unitarianism Originate?  ?

The original Unitarianism in the modern world arose as a kind of biblical recognition that the word Trinity is never used in the Bible, but was read into its interpretations. That occurred in Europe (primarily the UK), mainly in the 17th and 18th centuries, although there were pockets of the belief before then.  

Rather than say it's a false doctrine, perhaps, it is better said that based on their reading of the Bible, they saw no support for the Trinity. Personally, I see the Trinity as an effort by early Church Leaders to explain the multifaceted presence of the Divine. Actually, the Kabbalahists (originated in Jewish mysticism) do a more robust job of describing that concept. 

FROM SATAN THE FATHER OF ALL LIES

FYI your question is not a book title!  Learn how to use capitalization.

Harlem, 125th St. and Lennox Ave., 1929

The modern day Unitarians started:

In England, the first Unitarian Church was established in 1774 on Essex Street, London, where today's British Unitarian headquarters is still located.

The first official acceptance of the Unitarian faith on the part of a congregation in America was by King's Chapel in Boston, from where James Freeman began teaching Unitarian doctrine in 1784.

Those that go by the term 'Unitarian' are correct, when they say there is only only true God.  They are also correct when they say, God is not a trinity.

This teaching actually goes back to the teachings of Jesus, Peter, John and Paul. So one answer is it started in 29 CE with the baptism of Jesus.

The truth of the fact is was God not a trinity, goes back to the expression found at Genesis 1:1 "In the Beginning"

Or if you want to get truly accurate it goes back to the very beginning of time as God knows it, for Jehovah has always been and will always be the only true God, the Most High long before the spiritual and physical universe was conceived by Jehovah.

Sadly though the Unitarian restoration started out with the truth, they then incorporated many false teachings into their movements.

Such as God's word isn't infallible and there isn't an original sin.

On the other hand it is the Trinitarian teach the lie.

Some teach, God had to die to save mankind, yet God's word says the man Jesus died for us.

(Acts 2:22, 23) “22 “Men of Israel, hear these words: Jesus the Naz·a·reneʹ was a man publicly shown to you by God through powerful works and wonders and signs that God did through him in your midst, just as you yourselves know. 23 This man, who was handed over by the determined will and foreknowledge of God, you fastened to a stake by the hand of lawless men, and you did away with him.”

(1 Corinthians 15:20, 21) “ 20 But now Christ has been raised from the dead, the firstfruits of those who have fallen asleep in death. 21 For since death came through a man, resurrection of the dead also comes through a man.”

(1 Corinthians 15:45) “. . .: “The first man Adam became a living person.” The last Adam became a life-giving spirit. . .”

Since God cannot die, God could not have died for mankind.

If a person believes 'God died for them, then they are still in sin, because again, God CANNOT die.

It is the trinity and the trinitarian who are worshiping the false god, a man made teaching influenced by Satan.

Unitarians though they are wrong in many of their teachings didn't get the teaching of the only true God wrong.

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January 22, 1556, in Secemin, Poland.  It wasn't called "Unitarianism" until a hundred years later.

"false doctrine"   Tee hee.

Why Are You Capitalizing The First Letter Of Every Word You Write, Half-Wit?