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.
Another’s is the correct possessive form of another. We need to use “another’s” when we want to say that “another person” owns something.
One man’s trash is another’s treasure.
One man’s poison is another’s meat.
Anothers and Anothers’
Anothers and Anothers’ are not possible in English because another means “one more”. The correct plural is others which means a higher number more.
How do you use another’s?
You can use another’s when you want to say that a different person owns something else from the previous subject mentioned.