Recovery of permanently deleted photos

Please read the following user tip and restate your question/problem in detail: 

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1 - What device are you on - model and year?

2 - What system are you running on the device?

3 - Do you have any backups of the device and the library?

4 - Are you using iCloud Library?

If the answer to #3 & #4 is no then the photos are permanently gone.

You don't, that is exactly what permanently deleted means. When you received that warning when attempting to delete from the Recently Deleted folder, that was your chance to save the photos in another location in case you ever wanted to see them again.

I assume you are on an iPhone. With a Mac, you may have some options as far as backups, but it is unclear if that is the case.