I had a iPhone X in Jan. I sold it and backed it up to iCloud. I bought a new iPhone now after ten months. I want to restore my backup but it isnt showing up when i set my phone up.

Are you using the same Apple ID you were using on the iPhone X?

Also, what steps did you follow to make that backup?

Sounds like maybe you never made the backup, or you used the temporary backup option

Backups should remain on iCloud until replaced by a different one. The only exception to this, is if you used the temporary backup option.

Get temporary iCloud storage when you buy a new iPhone or iPad - Apple Support

If you don't have enough iCloud storage, you'll see a message that says

you're eligible to get free extra iCloud storage. Tap Continue.

If you saw the message above, and accepted, that backup only lives on iCloud for 21 days, after which time it is deleted.

Nope. New iOS versions can access backups made on older iOS versions just fine.