Doctor Who Magazine (in-universe)

Doctor Who Weekly, (PROSE: A Letter from the Doctor (DWM 1)) later named Doctor Who Magazine and also abbreviated to DWM, was a publication that celebrated the Doctor Who series. (PROSE: A Letter from the Doctor (DWM 500))

The publication also had a comic strip by 2013. (PROSE: A Letter from the Doctor (DWM 464))

History
The Fourth Doctor once wrote and dispatched two letters at a post office on Ganymede on 42 Paztenmber, relative to 1845 "Earth-time", as the Doctor wanted to ensure his letters arrived in time to be printed in the first issue of Doctor Who Weekly. In the first letter, the Doctor talked about several features in the magazine and recommended the 879th issue, and in the second letter, the Doctor explained how to use the rub-down action transfers included in the 1st, 2nd, 3rd, and 4th issues on two colour panoramas illustrated by Dave Gibbons. (PROSE: A Letter from the Doctor (DWM 1))

In 2013, Peter Capaldi (who had been recently cast as the Twelfth Doctor) wrote a letter to DWM, and he wrote about how good DWM had been to him thoughout his life. (PROSE: A Letter from the Doctor (DWM 464))

On 29 April, 2016, Peter Capaldi was requested to write a letter for the 500th, as well as either the 1,000th or 100,000th issue, but the actor couldn't remember which.

In his letter, he wrote about how he was proud about the magazine and how it inspired fans to "write their own stories, draw their own pictures, and make their own music and films". (PROSE: A Letter from the Doctor (DWM 500))

On 10 May 2020, a desktop icon was seen on Petronella Osgood's laptop. (WC: The Zygon Isolation)

Alternate universes
There also existed a Doctor Who Magazine in a universe where the Doctor was entirely fictional. (PROSE: The Thief of Sherwood) Doctor Who Weekly also existed in a meta-fiction universe where the adventures of the Doctor were also fictional. (COMIC: TV Action!)

Behind the scenes
This is clearly a reference to the real world magazine, referencing logos used in the 90s (note that color might change with each issue, so while the particular colors shown here might not be present in one version of the logo, that doesn't preclude them from being present in another).