How to recover permanently deleted videos

Where was it backed up? iTunes or iCloud?

Your post does not specify exactly the process adopted by you to take a backup.

If it is not in the Recently Deleted Album then either you have deleted them 30 days earlier or have never deleted any.

Please check the following

1. If you have restored your iPhone with a backup which does not contain the Photos that you are looking for then please look for correct backup on your PC/Mac --> Locate backups of your iPhone, iPad, and iPod touch - Apple ...
2. If you have restored from iCloud backup, then note the following
   1. iCloud backup doesn’t include information that is synced and stored in iCloud, like Contacts, Calendars, Bookmarks, Mail, Notes, Voice Memos, shared photos, iCloud Photos*, Health data, call history, and files you store in iCloud Drive.
   2. *-If you had turned on iCloud Photos, your content is automatically stored in iCloud. 
3. Probably you may have un-synced photos with Mac / PC, sync them again
   1. For PC: --> Sync photos in iTunes on PC with devices - Apple Support
   2. For Mac --> Sync photos between your Mac and iPhone or iPad - Apple ...
4. Have you ever imported your photos to Mac/PC and used Delete after Import --? Transfer photos and videos from your iPhone, iPad, or iPod ...
5. Do you have a backup (iTunes) --> Restore your iPhone, iPad, or iPod touch from a backup ...
6. Have you ever uploaded them to any Cloud Drives Cloud Drives (iCloud Drive, Google Drive, One Drive, Dropbox, Flickr, box, Amazon Drive, Adobe Creative Cloud etc.?)
7. At last but not the least, check the Apple ID that you have signed into your device.