How to recover permanently deleted videos and photos?

A great safety feature on the iPhone is that deleted pictures remain in the "Recently Deleted" view for 30 days before they are removed permanently. This safety feature can be defeated, though, by choosing to prematurely delete pictures from the "Recently Deleted" view.  If you use iCloud Photos, then that "synchronizes" its Photos Library with the phone, so what you see on the phone is what is at iCloud. iCloud Photos doesn't keep pictures in "Recently Deleted" any longer than the phone does. So it's really important to look carefully at the Recently Deleted pictures before deleting them permanently.There is no additional safety feature in case we don’t heed the warning for the first safety. Pictures that are deleted from the Recently Deleted view are permanently erased. 

You didn't give us much information You can see this:

        If you're missing photos or videos in the Photos app

Basically the above says to look in Recently Deleted and in Hidden. Be sure to check your Library thoroughly. You can use the search field with the date or location—the pictures may not be where you expect, as dates may have changed. And remember, you can sort the Library by date captured or by date added. Also, your Library view now has filters, and you may not have your filter set to "All Items.”

If you don't use iCloud Photos, but you have Settings>Apple ID>iCloud Backup turned on, then you may be able to recover data. You should look here:

Restore your iPhone, iPad, or iPod touch from a backup - Apple Support 

“Restore” is what you do when you buy a new phone, so this safety, if you have it set, requires you to erase everything on your phone and replace it with the backup. You would have to get to the backup quickly, usually within a day, before the backup is replaced by a newer one. However, if you did have iCloud Photos enabled, then the iCloud Backup wouldn't make an extra copy.

Perhaps you have shared your pictures with friends-- then you could get them to send copies back to you.

Unfortunately, if you don't keep your own backups to an external drive, then there really isn't any place else to look. To back up your pictures you can just plug in an external drive, select the pictures, and use Share>Save to Files. Alternatively, you can backup to a computer:

Transfer photos and videos from your iPhone or iPad to your Mac or PC

If you haven't done one of those backups, then your remaining pictures continue to be in peril. 

Hi Userlala2

You cannot recover permanently deleted photos. If you recently deleted it, you will have 30 days to recover it from “Recently Deleted”, after that it will be deleted forever and you cannot get it back.

Sorry, but your question is self-answering.

“Permanent” means permanent.

If you were backing and archiving up onto a Mac (with possibly a Time Machine backup of the Mac as well) you might have other options.