Year’s, Years’, and years are in fact all correct depending on the context.
Years is used for the plural of year. year’s and years’ are used in compound time expressions. Year’s is used with a singular time unit and years’ is used for a plural unit.
Year’s and years’
One year’s experience
Two years’ experience
You need to place the apostrophe before the s when you are writing about a singular time(one day, one year, one year) and after the s when it is a plural time(two days.Three years, four years)
Notice that we only need to do this when we include the noun that the time expression is about(possessive). We only do this when we can replace the apostrophe with of.(Read about when to use of in English grammar here).
One year’s free insurance
Four years’ free insurance
She is going away in one year’s time.
She is going away in two years’ time.
He was docked one year’s pay.
He was docked two years’ pay.
You can always use of if you feel like this makes things clearer:
He was docked one year of pay.
He was docked two years of pay.
In this case, years returns to a regular singular/plural noun.
If there is no noun that the time expression is connected to then years acts like a regular noun and you just need to add an s to make it plural.
I need to start work in one year.
I need to start work in two years.
Compound adjectives with year
Compound adjectives are when we combine two words with a hyphen to describe another noun.
He took a two-year holiday.
The package includes a one-year safari.
For compound adjectives, it is not necessary to add an s but it is necessary to add the hyphen.