Humans consider Leshp (an island, as Detritus remarks, without its teeth in) an uninhabited continent that occasionally comes back up to surface, and when Leshp does come up, countries around the Circle Sea fight over it. Ankh-Morpork on the Sto Plains and Klatch on the continent Klatch almost had a war over Leshp during the events of Jingo, where it was discovered simultaneously by the Morporkian fisherman Solid Jackson and the Klatchian fisherman Greasy Arif. Unfortunately, regardless of the effort that these countries put in to secure Leshp, it always disappears again. Since Leshp spends most of its time underwater, it is in fact a city for the Curious squid. The fabled brass gongs of Leshp can be heard far out to sea on stormy nights, as mentioned in Mort.
This cycle of rising and sinking is caused by a critical buildup (and ultimate dispersal) of sulfur-smelling gases in the gigantic hollow cavern beneath Leshp, and facilitated by the fact that its foundations are mostly tufa and pumice. For some reason, the place is covered in towering cyclopean ruins and pictures of octopi. More orderly and familiar architecture also appears, but seems to have been added at a much later date by different builders.
Leshp may be based in part on the Roundworld island of Ferdinandea, an island near Sicily that rises above sea level after periodic volcanic eruptions, only to disappear again after it is sufficiently eroded. When it made its most recent appearance in 1831, it was claimed as territory by four nations (The United Kingdom, France, pre-Italian-unification Naples, and Spain).
Well, that explains the territorial feuding part, yes. However a city of squid-creatures that has lots of squiddy art about the place and occasionally rises to bedevil humanity also echoes R'lyeh, home of Great Cthulhu.
To add a third level of annotation, a theme of Robert Shea and Robert Anton Wilson's Illuminatus! trilogy concerns the world being brought to the brink of World War Three, over ownership of the hitherto disregarded island of Fernando Poo. Manipulated by the evil Illuminati, the Russians, the Chinese and the Americans each claim that their legitimate sphere of interest is being interfered with, and one of the others must have destabilised a friendly sovereign nation by starting that coup d'état. (Meanwhile, the British don't want another bloody damn war, not when we've only just paid for the last one, North Sea Oil's coming on stream, and the balance of payments is straightening itself out). It falls to the intrepid crew of the free submarine Leif Eriksson to sort things out... a submarine, whose crew are on a mission to prevent war breaking out over ownership of a previously unknown and disregarded island. Hmmm...
"Fernando Poo" really exists, in the Bight of Africa on the Atlantic coast. Initially named after its Portuguese discoverer - a man with something in common with Ponce da Quirm - independence saw it retitled Sao Principe. Shea and Wilson use it as a gateway to a Lovecraftian world of squid-creatures, Unmentionables, and makers of eldrich and evil artistic artefacts.
Strangeness upon strangeness. The current edition of strange-things magazine Fortean Times (FT297, February 2013) has an article about the strange case of the Pacific atoll Sandy island, nominally halfway between Australia and French Caledonia. It has appeared on maps since the middle 1800's, and its existence was confirmed to the extent that it appears on Royal Navy sea-charts. It also appears in the Times Atlas of the World and even Google online maps list it. Its ownership is not disputed - it belongs in perpetuity to France as an overseas dependency. The only problem is - it has disappeared. An Australian Navy surveying ship reported nearly 5,000 feet of sea where the island was reported to be. Puzzlement has been expressed.