How to recover permanently deleted photos on iPhone?

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.”

As Servant of Cats has said, iCloud Photos doesn't keep Recently Deleted pictures any longer than your phone. However, 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. 

Permanent means just that.

If you have permanently deleted your photos, you cannot get them back from the iPhone. If you were using iCloud Photos, you do not get them back from iCloud or from other devices synchronized to your iPhone, either. Deletes synchronize the same way that other things do.

Your only hope would be if you had backups outside the system, backups made before you permanently deleted the photos in question.