"Ain't no such thing", alt. "Used to be all of it".
As I understand it for me the territory where my "folks" came from was a Finnish island under Swedish rule (I don't remember which island at this point.........There's no such thing as "a Finnish island under Swedish rule"; there haven't been any border disputes for pretty much exactly two centuries now, so all islands under Finnish rule are Finnish and all islands under Swedish rule are Swedish. Oh, sure, there are pockets of the opposite *language* (and thus I guess you could say "*culturally* Finnish islands under Swedish rule") in both countries... but everybody is pretty much satisfied with the citizenship they have; I know for sure that Finland-Swedes cheer on Finnish, not Swedish, athletes at international competitions.
Unless you mean your ancestors emigrated before 1809; then *all* Finnish islands -- as well as the mainland -- were "under Swedish rule", because they were just simply a part of Sweden. But that was no kind of *foreign* "rule" (as your way of putting it seems to imply); there never was an independent entity "Finland" before the Czar created the semi-autonomus Grand Duchy out of his newly-acquired ex-Swedish territories.