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3 year's / 3 years' experience.

The correct form is "3 years". The experience does not belong to the year.
It belongs to the applicant. "years" is just a simple plural. It is not a
possessive.

Re: 3 year's / 3 years' experience.

No, I'm sorry. You're not right on this occasion, but I do understand your logic.

It's called a temporal expression. The apostrophe is correct.