The standard form of the word meaning long life or duration of life is longevity. The centuries-old word comes from the archaic adjective longevous, which in turn derives from the Latin longaevus, meaning long-lived or ancient. In early use, it was sometimes longaevity, but that has been its only recognized variant.
Longetivity is a rare form that appears on the web about once for every few thousand instances of the shorter form. It probably comes about by analogy with similarly ending words such as positivity and activity. It doesn’t appear in any of the major dictionaries, and it has never been common. Google Books uncovers a few published instances from the 1990s and none from before that, EBSCO finds a few in journal articles from the 1950s and ’60s, and, somewhat interestingly, there is a 1930 Harvard Crimson article called “Longetivity and Sportsmanship,” which uses “longevity” in the article body, suggesting the form in the title is some sort of error.