Faith Smith is the daughter of Culverton Smith. She walks with a cane but it isn't explained if it was caused by an accident or illness. In the episode her appearance and identity were stolen by Eurus Holmes as part of her scheme.
Faith first appears in a part of a flashback where she is attending a meeting with her father and some of his friends. Her father hooks up all the attendees with a drug which will wipe their short term memory, causing them to forget the events of the meeting, and then using this to confess to being a serial killer.
Faith is horrified by her father's confession and, whilst visibly showing signs that the drug is working on her, attempts to write down what she remembers about the meeting on a piece of paper. Her father catches her and confiscates the paper from her while the drugs continues to wipe her memory.
Faith is shown to have a very strong moral compass, as shown when she tries to write down what she could remember about the meeting, despite it being incriminating evidence against her father. Eurus's impersonation of her depicts her as introverted and suicidal, though she seems to have a sense of humor as well, shown when she sasses Sherlock.
Faith seems to have a good relationship with her father as she is open and friendly towards him when she arrives in the Hospital when summoned by the text Sherlock sent from her father's phone. She asks if the text was "one of his jokes", implying a playful relationship.
However, like most people would be, she is horrified when her father confessed to her and the other people at the meeting and even tried to take steps so that she would remember her father's confession.
She ends up being impersonated by Sherlock's sister, Eurus.