Susan Foreman's father

The father of Susan Foreman was a Time Lord of the first rank and a Cardinal. He was the eldest of the thirteen children of the Doctor and Patience. He lived in the House of Blyledge with his family. On the day that his wife was giving birth, Lord President Rassilon sent guards to terminate the pregnancy, as it had been decreed that only the loom-born could inherit the legacy of Rassilon. The First Doctor travelled to the past and saved Susan and Patience. (PROSE: Cold Fusion)

Susan's father died in battle on one of Rassilon's bowships. (PROSE: Lungbarrow)

In an account where Barbara Wright was Susan's tutor, (PROSE: Doctor Who in an Exciting Adventure with the Daleks) rather than her teacher at Coal Hill School, (TV: An Unearthly Child) Susan told Barbara that she hadn't seen her mother and father in a long time. (PROSE: Doctor Who in an Exciting Adventure with the Daleks)

Potential identities
According to some accounts, Susan was the daughter of the Lord President of Gallifrey. (PROSE: A Brief History of Time Lords, TV: Hell Bent) One account says that Pandad VII was Lord President of Gallifrey around the time the First Doctor and Susan left Gallifrey. President Pandad VII ordered Lord Burner Braxiatel to burn "an old man" and "his granddaughter" from history. He disobeyed this order and the intended victims stole a TARDIS and fled Gallifrey. The very same day, President Pandad died when a power relay in his office overloaded; an inquiry headed by Braxiatel found that this was an accident. (AUDIO: Disassembled)

According to a conflicting account, Slann was Lord President of Gallifrey during the time the First Doctor and Lady Larn, a descendant of Rassilon, left Gallifrey. He was assassinated by the Master shortly after. (PROSE: Birth of a Renegade) Curiously, another account spoke of Pandad IV as a President postdating the Doctor's departure from Gallifrey. (PROSE: The Legacy of Gallifrey)