Timeless Child

The Timeless Child was a title used to refer to the mysterious being from whom, across several regenerations, Tecteun's original incarnation extracted the secret of regeneration. According to the Spy Master, the Timeless Child's incarnations were none other than the original incarnations of the Doctor from a previous life long before the First Doctor. The Master also confirmed that the Doctor's memories had been erased by the Division, making the Doctor relive their childhood.

Discovery
The Timeless Child was a being of an unknown species discovered by Tecteun on another planet. The child had been waiting beneath a wormhole when Tecteun found her. (TV: The Timeless Children) A later incarnation of Tecteun explained that the wormhole led to a universe dubbed Universe Two, and theorised that this universe might have been or contained the Timeless Child's realm. The Thirteenth Doctor was less certain that this was the case, however. (TV: Survivors of the Flux)

The child was adopted by the First Tecteun, who discovered the child's power to regenerate after she suffered a fatal fall from a cliff and regenerated before Tecteun's eyes. Tecteun went on to study the child's power for a number of years and regenerations, which led to a total of at least seven incarnations. (TV: The Timeless Children) During this time, the child referred to Tecteun as "Mother", while Tecteun regarded them as her "experiment". (TV: Survivors of the Flux)

Tecteun was eventually able to replicate this regenerative ability, regenerating herself into a new incarnation. The Second Tecteun eventually spread this power to other Shobogans, who would go on to become Time Lords. He also artificially limited the number of regenerations to a maximum of twelve.

In the process, the Timeless Child became the genetic template upon which all Time Lords were modelled, giving them their characteristic regenerative abilities. (TV: The Timeless Children)

Service to the Division
Tecteun and the child were inducted into a clandestine organisation called the Division, led by a Time Lord called Solpado, whose job it was to intervene in time when necessary. After being tested, the results came back saying they were the best the Division had ever seen. Upon completion of the child's, later known as the Doctor's, service, their memories were redacted and they were forced into the form of a child, who grew up to become the First Doctor. (TV: The Timeless Children)

Legacy
Richard Francis Burton once guessed that the Great Houses (PROSE: The Book of the War) of the Time Lords (PROSE: Lungbarrow, et. al) had achieved the power of regeneration by modifying themselves with the "taint" of the Yssgaroth, (PROSE: The Book of the War) much like how the account involving Tecteun and the Timeless Child involved the former taking biodata from the child and applying it to Time Lord DNA. (TV: The Timeless Children) Indeed, the vampires active in the universe were searching for a Child-That-Was-Taken. (PROSE: Out of the Box)

According to the Spy Master, the Founding Fathers of Gallifrey built Time Lord society on a lie regarding the Timeless Child. This was buried deep within all Time Lords, in the form of repressed thoughts and memories: hidden, but integral to their identities. (TV: Spyfall) He later expanded upon this stating that an individual known as the "Timeless Child" was discovered and whose ability to regenerate was written into the genetic code of Time Lords. This history was subsequently hidden, with another explanation being given for this ability instead. This was the mythology all Time Lords believed was their history. (TV: The Timeless Children)

To contain the secret, large portions of the Matrix on Gallifrey pertaining to the life of the Timeless Child were redacted, beyond the Master's ability to recover them, even after the fall of Gallifrey. However, Tecteun hid some of the truth in the Matrix in the form of the story of Brendan, an immortal Irish policeman. The Master suggested that this was an attempt by Tecteun to apologise, or possibly meant as a gift, to help her child one day work out the truth of their existence. (TV: The Timeless Children) A later incarnation of Tecteun told the Thirteenth Doctor she did not wish them to find out, however, as she feared the Doctor's reaction. (TV: Survivors of the Flux)

While taunting the Thirteenth Doctor about her fears, Remnants on the planet Desolation looked "further back" into her past and referred to the Timeless Child. When they made the reference, the Doctor was confused and asked them what they were talking about, then angrily told the Remnants to "get out of [her] head". (TV: The Ghost Monument)

Once the Master learned the truth about the Timeless Child, he ravaged Gallifrey to "make them pay" for what he discovered. He told the Thirteenth Doctor that learning the truth had not been easy for him. (TV: Spyfall) He was enraged that every Time Lord had a piece of the Doctor in them, including him.

On Gallifrey, he told the Thirteenth Doctor the truth about her past. (TV: The Timeless Children) She suffered an identity crisis for a number of years while carrying out a prison sentence in the Judoon prison - but upon breaking free, she rediscovered herself during her next battle with the Daleks, (TV: Revolution of the Daleks) who had been central to the formation of the First Doctor's identity. (TV: The Magician's Apprentice)

The Doctor would continue to pursue information about her lost past, however, by searching for the last known member of the Division, Karvanista. (TV: The Halloween Apocalypse) After the Flux damaged the Temple of Atropos, the Doctor relived the Siege of Atropos from the Fugitive Doctor's perspective and encountered a later incarnation of Tecteun within her own time stream during her attempt to remedy the time storm she found herself in. (TV: Once, Upon Time) It was later when the Doctor was recalled to Division by the Weeping Angels that Tecteun confirmed the story of how she found the Timeless Child. (TV: Survivors of the Flux)

Later, the Ravager presented the Doctor to Time as a sacrifice, proclaiming her as "the Timeless Child". (TV: The Vanquishers)

By the time of his fourteenth incarnation, the Doctor still wondered about the truth of the Timeless Child. (TV: Wild Blue Yonder)

Behind the scenes

 * Out of the Box's mention of a "Child-That-Was-Taken" referenced the fan theory that the Timeless Child originated from the Spiral Yssgaroth and her abduction by Tecteun was the reason for the Eternal War between the Great Vampires and Gallifrey. Author Aristide Twain explained that for both creative and legal reasons, this suggestion wasn't meant to be definitive: "If you’d rather believe the Child-That-Was-Taken is something else entirely, who am I to stop you?"