There’s no Java collection in the standard library to do this. LinkedHashSet<E> preserves ordering similarly to a List, though, so if you wrap your set in a List when you want to use it as a List you’ll get the semantics you want.
Alternatively, the Commons Collections (or commons-collections4, for the generic version) has a List which does what you want already: SetUniqueList / SetUniqueList<E>.