In the Anglo-Saxon Chronicle, Cissa is listed as one of the three sons of Ælle, who in the year 477 arrived in Britain in three ships with his three sons, and fought three battles, but "Modern scholarly opinion does not accept this dating". Most authorities recognize that these annals are not contemporary with the events they record, but were compiled in 891. Morris accepted these annals as historical, but then undermined his own position by disputing their accuracy: “in west Sussex, the first English graves are more than a hundred years later. Chichester is not called Elchester from Aelle, but bears the name of one of his three ‘sons’; the earliest English object in the area is a brooch found in the Roman cemetery of St. Pancras, that dates to the time of Aelle’s grandchildren. Its isolation suggests a Saxon woman who lived and died in a British community rather than a Saxon settlement. The absence of pagan burial grounds in west Sussex argues that the English did not reach Chichester until more than a hundred years after Aelle’s time; Cissa was more probably his remote heir than his son”.
Roger of Wendover even went so far as to provide a death date for Cissa, that had previously been absent. The date he gave was 590, which, given that Cissa is supposed to have arrived in Britain in 477, means that he must have been more than 123 years old at the time of his death. As Kirby & Williams observed "It seems very unlikely that these annals in later medieval chronicles will provide a certain basis for historical reconstruction".
Another place name potentially associated with Cissa is the Iron Age hill fort Cissbury Ring, near Cissbury, which William Camden said "plainly bespeaks it the work of king Cissa". Yet its real date precludes any such connexion, and furthermore there is a record from 1663 in which it was called "Cesars Bury". It seems that ties between Cissbury and Cesars Bury and Cissa are nothing more than back-formations: Cissbury has been identified with a Saxon mint, “the implied Sith(m)esteburh of Saxon coinage, ‘the last built burh’." Indeed, "[e]very association of the original name with Cissa son of Ælle is fanciful.”