Poseidonia was the original name for the Roman city of Paestum, situated south of Naples, founded by Greek colonists around 600 BC. It was partly flooded and largely forgotten until a number of well-preserved Greek temples were rediscovered in the 18th century.
Coincidentally, the city was established in a region of southern Italy, described by Plato as being part of Atlantean territory!
Thomas Major (1720-1799), a royal engraver, visited the site in 1767 and described the ruins of Paestum in an illustrated 1768 book, The Ruins of Paestum, otherwise Posidonia, in Magna Graecia .
Poseidonia, is also the name of a village on the Cycladic island of Syros.
Poseidia was the name given to largest island of the Atlantis archipelago by Edgar Cayce and his followers. It is not a name mentioned by Plato or, as far as I’m aware, any other ancient writer.