The Book of the New Sun was only the start of the story, Gene Wolfe went on to write a further volume about Severian and then two further series set in the same universe.
The Urth of the New Sun is set several years after the events recounted in the quartet. Severian is now travelling in a massive spaceship to meet the all-powerful alien who can rejuvenate Urth's dying sun. Along the way he has to encounter all the dead people he has known, and, upon his return to Urth, he finds himself once again facing the enemies he had to battle in the first quartet.
The Book of the Long Sun is another four-book series, Nightside the Long Sun, The Lake of the Long Sun, Call of the Long Sun and Exodus from the Long Sun, which follows the adventures of Patera Silk. As the series opens he is a lowly priest in a small neighbourhood 'manteion', but in his efforts to save the manteion he discovers that he is actually aborad a generation starship now nearing its destination.
The Book of the Short Sun concludes what has been known as the 'Solar Cycle' with three novels, On Blue's Waters, In Green's Jungles and Return to the Whorl. A direct sequel to The Book of the Long Sun, the plot concerns the search for Patera Silk across the two habitable worlds, Blue and Green, that the generation starship Whorl has reached. By the end of the sequence we realise that these events immediately precede
If you love Gene Wolfe's allusive writing and subtle world building, then don't miss The Fifth Head of Cerberus. These three linked novellas concern two planets once colonised by the French, where the population has a rich if rather decadent lifestyle. But there's a mystery concerning the aboriginal inhabitants of the planets who seem to have disappeared, but who are rumoured to have been shapeshifters. Could the humans actually be the natives in disguise?
As The Fifth Head of Cerberus indicates, before he embarked on The Book of the New Sun Gene Wolfe was best known for his multiple award-winning stories, many of which are gathered in The Best of Gene Wolfe; look out in particular for "The Island of Doctor Death and Other Stories", "The Death of Doctor Island", "Seven American Nights", and "The Hero as Werwolf".
The dying earth that we encounter in The Book of the New Sun has a long tradition in science fiction. Don't miss the book that gave its name to the subgenre, The Dying Earth by Jack Vance, set in a distant future when the Moon has disappeared, the sun is burning out, and predatory monsters from another age now infest the cold and barren landscapes of Earth.