I assume you mean you could only access your last 3 backups. If you were not using iCloud Photo Library and those photos were not included in any of those backups, then I am afraid the photos are gone for good. If you were using iCloud Photo Library, then the photos are not included in your backup anyway. See Note 1 in:
What does iCloud back up? - Apple Support
I suggest, in the future, that you regularly archive your photos to a computer and then copy them to a safe place (like a thumb drive):
Transfer photos and videos from your iPhone, iPad, or iPod touch - Apple Support
By any chance have you made any backups of your device using iTunes on your computer?
About backups for iOS devices - Apple Support