The possessive pronoun “one’s” requires an apostrophe before the S, unlike “its,” “hers,” and other personal pronouns. Examples: “pull oneself up by one’s own bootstraps,” “a jury of one’s peers,” “minding one’s own business.”

A simple test: try inserting “anyone’s” in place of “one’s.” If it works grammatically, you need the apostrophe in “one’s” too. When “one’s” is a contraction of “one is” it also requires an apostrophe: “no one’s listening,” “this one’s for you.”

The only times “ones” has no apostrophe are when it is being used to mean “ examples” or “people” as in “ripe ones” or “loved ones,” or in the informal arithmetical expression “the ones column.”