The Doctor's species

Much like their age and the true circumstances of their early life, the Doctor's species was a matter of much contention due in part to shifting timelines. (PROSE: Celestial Intervention - A Gallifreyan Noir)

Time Lord

Although human-like in appearance and broad mannerisms, the Doctor was by most accounts not human; (PROSE: Who is Dr Who?) the Doctor usually identified themselves as a Time Lord (TV: The War Games, Pyramids of Mars, The Night of the Doctor,etc.) from the planet Gallifrey in the constellation of Kasterborous. (TV: The Day of the Doctor)

A previous life, a previous race

According to one account, however, the Doctor's childhood on Gallifrey with the Master was a result of their having been regressed into a child, and their memories redacted, after a large number of regenerations; they were originally the Timeless Child, a being of an unknown species whom the Shobogan explorer Tecteun adopted and brought back to Gallifrey, harnessing the Child's regenerative abilities to turn her people into the Time Lords. Though she sequenced her adopted child's entire DNA, Tecteun was still no closer to discovering the true origins of the Doctor. (TV: The Timeless Children)

In a similar but distinct account, the First Doctor was indeed the first incarnation of the Doctor as such, but was the reincarnation of the Other, one of the Founders of Gallifrey, whose mind and genetic structure had been redistributed into the Loom which created the Doctor many millennia later. (PROSE: Lungbarrow) According to The Thousand and Second Night, a highly figurative account written in the style of Middle Eastern folktales, the Other was was "neither an angel nor a djinn". (PROSE: Head of State, Interference)

Half-human?

The Eighth Doctor had vivid memories of his childhood with his father on Gallifrey, but also claimed to be half-human on his mother's side; the Bruce Master's analysis of the Doctor's retinal structure seemingly confirmed this, (TV: Doctor Who) although the Eighth Doctor would later claim that he had tricked "his greatest enemy" into thinking him to be half-human using a "half-broken Chameleon Arch". (COMIC: The Forgotten)

Human

In other accounts, the First Doctor and the Second Doctor were identified as human beings (PROSE: Doctor Who and the Daleks) whose regeneration powers were a function of the TARDIS they piloted. (TV: The Power of the Daleks) The Daleks believed that it was as a result of his many travels through Time that the Doctor had become "more than human". (TV: The Evil of the Daleks)

One account referred to the Doctor as the greatest human mathematician, whose equations had at long last united Space and Time fully into the inextricable concept of the Idea of the Living Matter. This had allowed him to construct the TARDIS, a machine which could withstand and travel through Eternity and Infinity in a microsecond. (PROSE: The Equations of Dr Who)