According to the 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 discoverd and whose ability to regenerate was written into the genetic code of Time Lords. This history was subsequently hidden, with another explanation, a lie, being given for this ability instead. (TV: The Timeless Children).
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. When the Master first mentioned the Timeless Child mystery to the Doctor, she got a massive headache and a flashback to when the Remnants approached her, as well as a glimpse of a child wearing yellow robes and standing outside a tall building under a purple sky. (TV: Spyfall)
While aboard a space platform in the far future owned by Zellin, the Doctor, after having fallen unconscious due to Zellin's powers, dreamed about the vision of the Timeless Child while the Master's message to her echoed in her mind. In this scenario she was actively present in the vision. (TV: Can You Hear Me?)
The Timeless Child was eventually revealed by the Master to be a child discovered on another planet who had the power to regenerate infinitely who had come through a gateway from another universe or dimension. The child was adopted by Tecteun who discovered her power to regenerate after she suffered a fatal fall from a cliff, leading to Tecteun studying the child's power for a number of years and regenerations. Tecteun was eventually able to replicate the regenerative ability for herself and eventually spread it to the other Time Lords, though they limited their number of regenerations to twelve. In the process, the Timeless Child became the genetic template upon which all Time Lords gained their regenerative powers, in effect meaning that a piece of the child is in each Time Lord.
The Master revealed to the Doctor that the Timeless Child was in fact the Doctor themselves who apparently had her memories redacted. In addition, large portions of the Matrix on Gallifrey pertaining to the life of the Timeless Child were also redacted beyond even the Master's ability to recover it. 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 apologize or possibly a gift meant to help her child one day decode the truth of their existence. (TV: The Timeless Children)