Prefer whoever and whomever to whosoever and whomsoever, the latter two of which are wordier, are more antiquated, and have been less popular for over two hundred years.
Whoever is subjective and whomever objective (see who or whom). For the possessive cases, whosever used to be preferred, though whoever’s has dominated for almost a hundred years. But in strict usage, whoever’s suggests a contraction of whoever is or whoever has. If possible, rewrite the modern possessive to avoid confusion with the contraction.