The word “another’s” is correct when you want to say something belongs to another person. For example, “This is another’s book.” On the other hand, “anothers” and “anothers'” are not correct in any context.

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.