how much does it cost to repair my back glass if i have a limited warranty

It would have helped had you listed the model of your iPhone in your post.

For back glass replacement costs, click here 👉 iPhone Repair and Service

Axel F.

iPhone Repair - Official Apple Support

This should be helpful.

We are mainly an apple users forum, apple users helping other apple users

We cannot help you with this, I suggest you would ask this at your local Genius Bar