grammaticality - Can your's ever be used?

I have a specific sentence in which I feel inclined to use "your's" but in not sure if it's correct. Then sentence is:

"Every story has a beginning - This is your's."

What "your's" stand for here is simply "this is your story's beginning" but to spell it out like that doesn't create the same feeling.

Albeit, is this a correct usage of "your's"?

Edit: This is not a duplicate of "Yours vs your's" as I'm asking for a situation in which "yours" can't be used since it would mean their beginning, not their stories' beginning.