Peter Capaldi (in-universe)

Peter Capaldi was an actor who portrayed the Twelfth Doctor in the BBC series, Doctor Who. (TV: In the Forest of the Night, PROSE: A Letter from the Doctor 464, A Letter from the Doctor 500, WC: The Zygon Isolation) He thought that the Doctor was fictional, but was ultimately uncertain. (PROSE: A Letter from the Doctor 500) The real Twelfth Doctor greatly enjoyed Capaldi's acting and thought he was "rather handsome for his age". (WC: Peter Capaldi and Simon the Shy Cyberman Invite You to Breakfast with 7 Doctors)

Biography
Capaldi was born in the 1960s, and he grew up reading issues of DWM; this magazine was a treat in particular, due its inclusion of pictures and facts, which were rare among other magazines of the period. (PROSE: A Letter from the Doctor 464)

The Eleventh Doctor once claimed to have saved Capaldi from a Mandrel and that Capaldi would make a "a great [him]". (COMIC: The Girl Who Loved Doctor Who) Capaldi was cast as the Twelfth Doctor in 2013, where he attended a meeting with Steven Moffat. He prepared for this meeting by reading previous issues of DWM. Soon, he wrote a letter to the readers of DWM, going over his positive views of DWM. (PROSE: A Letter from the Doctor 464)

An advertisement for Doctor Who (with images of Capaldi, a female co-star, and the TARDIS) was applied to the side of a bus (TV: In the Forest of the Night) in November 2014. (PROSE: "Assessing the Risk")

Peter Capaldi played the Doctor in the ninth series, specifically in the episodes New Series Prologue, The Magician's Apprentice, The Witch's Familiar, Under the Lake, Before the Flood, The Girl Who Died, The Woman Who Lived, The Zygon Invasion, The Zygon Inversion, Sleep No More, Face the Raven, and Heaven Sent. The ninth series was broadcast starting in October 2015. (WC: The Zygon Isolation)

On 26 April 2016, Peter Capaldi wrote a letter for and requested by Doctor Who Magazine, which they printed in their five-hundredth issue. Capaldi was also asked to write a letter for another issue, but he couldn't remember which one. (PROSE: A Letter from the Doctor 500)

Alternate universes
Peter Capaldi also existed in a parallel universe where the adventures of the Doctor were solely fictional. The Eleventh Doctor suggested he play the Doctor to Matt Smith. (COMIC: The Girl Who Loved Doctor Who)

Behind the scenes
Lewis Capaldi, Peter Capaldi's second-cousin-once-removed, also exists in-universe. He was mentioned in passing in PROSE: The Shadow Passes. Evidently, "Peter Capaldi", in all above instances, was intended to be an in-universe version of the real Peter Capaldi, who portrayed the Twelfth Doctor. At the end of WC: Peter Capaldi and Simon the Shy Cyberman Invite You to Breakfast with 7 Doctors, a screen featuring photographs of each Doctor who would be present at the event, in-costume as "the Doctor", was featured. This may be taken as an in-universe representation of Capaldi.