Backups

Did you downgrade from the beta using the steps in this article? From the article below.

If you back up a device that has iOS beta to iCloud or iTunes, the backup won’t work with earlier versions of iOS. For example, if you go back to iOS 11.4.1 from iOS 12 beta, a backup you made while using iOS beta won’t restore. Instead, restore from a backup that you made before you installed iOS beta.

Beta software - How to install or uninstall iOS 

Do you mean restore to a backup taken from a device that's on higher iOS version ? If you do, you can't, the phone will need to be on at least the same iOS version as the backup.

What happens when you try to back it up ?

Have you got access to a different network you could try on ?

It should back up in the same way