Another’s is the correct possessive singular form of the word another. Anothers is incorrect because there is no plural form of another. Anothers’ is also not possible because there is no plural possessive of another. Another means one more and therefore there is no plural. If you need to use more than one more, then you can use others.

The possessive form of “another” is another’s, and there is no plural form. When referring to indefinite pronouns such as somebody, anyone, or nobody, you would use apostrophe +s in the possessive form (e.g. someone’s, anyone’s, everybody’s), even if you are referring to multiple people.