There is no evidence that any of Constantius's daughters married before their father died.[8] Anastasia's sister Constantia may have been the first to marry, and may have been the oldest of the siblings. Constantia married in 313.[8] Anastasia herself married Bassianus in 316[8] or in 314.[9] At that time, Anastasia's half-brother Constantine was emperor. He planned to make Bassianus caesar (a junior co-emperor). Anastasia's brother-in-law Licinius (Constantine's junior co-emperor) did not want this to happen, and Bassianus did not become caesar. After this Constantine executed Bassianus. The Anonymus Valesianus says that Bassianus's execution was because Bassianus planned treason.[9] What became of Anastasia is unknown.[2] The encyclopaediaBrill's New Pauly says that Anastasia "must have still been alive" when Constantine built the city of Constantinople, because of the Roman baths there with her name (Latin: Thermae Anastasianae).[10]
In the 5th century, the Greek historians of Socrates Scholasticus and Sozomen both wrote that the Thermae Anastasianae got their name from another Anastasia, a daughter of the emperor Valens. This information is not correct.[11]