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)
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. 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 dark-skinned 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. By bringing the child to Gallifrey and studying its power, the race that would become the Time Lords gained the ability for themselves, though they limited it to twelve regenerations per Time Lord. The Timeless Child was in fact the Doctor whose memories of their early history had been redacted. (TV: The Timeless Children)
Behind the scenes
The two young actors who played the second and fourth Timeless Children respectively are tied for being the first actors of East Asian descent to play the Doctor.