How can I retrieve permanently delete Photos on my iPhone?

The key word is "permanent". I assume you deleted them from your Recently Deleted folder and were meant with the warning that continuing that action will result in your photos being permanently deleted. If that is the case and you continued with that action then you will not be able to recover the photos. You would have needed to save them in another location before you deleted them off your phone.

What kind of backup are you keeping of your iPhone? The iCloud backup of your iPhone will only include your photos, if you have not been using iCloud Photos on your iPhone. If you are having a backup you made, before you deleted the photos (and have not been using iCloud Photos), you can recover your photos by restoring the iPhone from the backup. Restore your iPhone, iPad, or iPod touch from a backup - Apple Support

But this will revert everything to the way it has been, at the time you made the backup. So you have to make a current backup to save the current state without overwriting your older backup, before you restore the iPhone.