Yes, it is possible to permanently delete photos on iPhone. The reason some photos keep reappearing is that they may be synced to iCloud or your computer. Here's what you can do to permanently delete photos from iPhone:
1. Open the Photos app on your iPhone.
2. Go to the "Albums" tab and select the album containing the photos you want to delete.
3. Tap "Select" in the top right corner and select the photos you want to delete. You can select multiple photos at once.
4. Once you have selected the photos you want to delete, tap the trash can icon in the bottom right corner.
5. Confirm that you want to delete the photos by tapping "Delete [number] Photos."
6. The deleted photos will be moved to the "Recently Deleted" album, where they will remain for 30 days before being permanently deleted.
7. If you want to permanently delete photos iPhone before the 30-day period is up, go to the "Recently Deleted" album and select the photos you want to permanently delete.
8. Tap "Delete" in the bottom left corner.
9. Confirm that you want to permanently delete the photos by tapping "Delete [number] Photos."
Once you have permanently deleted photos on iPhone, they will no longer be available in your Photo Library or the Recently Deleted album. However, if your photos are automatically syncing to iCloud or other devices, you'll need to turn off iCloud syncing or delete the photos from those devices as well to ensure they are completely gone.