514 to 544. Legendary foundation of the Isle of Wight
The Anglo-Saxon Chronicle suggests that Stuf and Wihtgar fight the Britons in 514, that Cerdic and Cynric capture the Isle of Wight in 530 and kill some men at Wihtgaraburg, that Cerdic and Cynric give Wight to their kinsmen Stuf and Wihtgar in 534, and that Wihtgar dies and is buried at Wihtgaraburg in 544. This is almost certainly a tissue of later invention: written sources for the verifiable history of the Isle of Wight only take up the story in the 660s (see entry on 661).
One problem with the story is that the name of the character Wihtgar seems to be based on a misunderstanding of the placename Wihtgaraburg (Wihtgaraburg, perhaps originally Wihtwaraburg, means "fortress of the inhabitants of Wight", not "Wihtgar's fortress": see entry on c.450 to c.550). Another problem is the genetic association of Stuf and Wihtgar (using these probably made-up names as shorthand for "the Anglo-Saxon founders of the Isle of Wight") with the West Saxon royal line, since Bede states that the inhabitants of the Isle of Wight in his day are Jutes. Archaeology confirms this association with Jutish Kent rather than with Saxon areas (see Yorke, pp.88-89), as does the presence of what can only be the Latin name for the Isle of Wight, Uecta, in the Kentish genealogy recorded by Bede (HE, i.15). So we might more readily expect the founders of Wight to be linked with Hengest's line.
It is very likely that the association with the West Saxons arose at some point after King Ceadwalla of Wessex captured the Isle of Wight in 685, which Bede reports somewhat disapprovingly (HE, iv.16, and see Yorke, p.89). The connection had definitely been made by the late 9th century, when Asser notes in his biography of King Alfred (contemporary with the first appearance of the Chronicle) that Alfred's mother traced her descent to Stuf and Wihtgar. Asser (correctly) notes that they are Jutes, but also (implausibly) maintains that they are the nephews of Cerdic. It may be that the Jutish founders of Wight were "attached" to the West Saxon royal house to give Alfred's mother Osburh higher standing, either during the marriage or afterwards when Alfred's father Æthelwulf brought home a Frankish princess as his second wife. The children of the first wife may well have felt a need to bolster their claim by proving that they too were royal on both their father's and their mother's side.