The short answer: Massachusetts law says residents are officially called Bay Staters. “Massachusettsan” has appeared in federal style guidance, so the internet did not invent it—but it is not the Commonwealth’s official designation.
Massachusetts Actually Has an Official Answer
This is unusual because demonym arguments normally end with everybody yelling regional nicknames at one another.
Massachusetts General Laws, Chapter 2, Section 35 says: “Bay Staters shall be the official designation of citizens of the commonwealth.”
There it is. The legislature got involved.
So Where Did “Massachusettsan” Come From?
“Massachusettsan” is not fake. Federal style references have used it as the formal adjective/demonym for Massachusetts residents.
That is how you get two answers floating around at the same time: one from style-guide convention and one written directly into state law.
What Do People Actually Say?
Bay Stater is perfectly normal. Massachusetts resident also works and has the major advantage of not sounding like you lost a fight with a suffix.
And yes, New England has several less-formal options. I am not making the Massachusetts Legislature codify those.
What About People From Cambridge?
Residents of Cambridge are commonly called Cantabrigians, which is a separate local demonym and does nothing to make this topic less ridiculous.
The Verdict
If somebody asks what people from Massachusetts are officially called, the clean answer is Bay Staters.
If you see “Massachusettsan,” you are not looking at a typo. You are looking at the kind of word government style manuals produce when left unsupervised.