Hello fooladder, welcome to the forums.
Obvioulsy, with the possessive, you use the apostrophe.
It was a popular tune sometime back in the early 1990s.
He has 1990's biggest hit record. (Obviously, a possessive.) EDITED for clarity -by this I mean the one year, 1990.
He was the 1990s' most popular enteratiner. (Also possessive.) EDITED for clairty - by this I mean the decade of the 1990s.