- You may be looking for the clone created from the Fourth Doctor that came out as the Second.
Due to the hasty measures taken to create it, the clone was a short-lived "photocopy" created by the Kilbracken cloning technique. He had a maximum lifespan of eleven minutes. His mind contained memories and experiences of the original. The Doctor's outfit was copied as well.
He shared a connection with his "outside self", such that when the original Doctor felt pain, so did the copy.
While traveling through the Fourth Doctor's brain with Leela's Clone, he told her that the part of his brain called the Reflex Link had lost the ability to tune into the Time Lord Intelligentsia. (TV: The Invisible Enemy)
In 5000, the real Doctor had put himself in a self-induced coma at the Bi-Al Foundation to prevent the Swarm from taking control of his mind and spreading his virus across time and space as their "carrier". He instructed Professor Marius to take blood samples from Leela and himself to create cloned copies of them both. Like the original, the cloned Leela was immune to the Swarm. (TV: The Invisible Enemy)
Entering the mind
The clone Doctor took the relative dimensional stabiliser from the original's TARDIS to shrink himself and the clone of Leela. Professor Marius injected the shrunken Doctor and Leela into the real Doctor's brain. If possible, they intended to exit the real Doctor's body through the tear duct. While searching for damage, Leela was attacked by phagocytes; the Doctor interfered with the real Doctor's brain to drive them off.
They crossed the mind-brain interface, where he confronted the Nucleus, objecting to the Swarm's ways. The Doctor's lifespan ran out shortly afterwards, and he dissolved. His lingering thought of getting to the tear duct enabled the Nucleus with a means to escape the microscopic world. (TV: The Invisible Enemy)