A Microsoft file hosting and synchronization service.
If some of your older photos are still appearing in "On This Day", it suggests that OneDrive may still have metadata or copies of some of those files, even if they aren't visible in your main Photos view.
A few things you can check:
Browse My Files, especially folders such as Pictures, Camera Roll, or SkyDrive Camera Roll, instead of relying only on the Photos tab.
Use the OneDrive search feature to look for an older photo by file name or date, if you remember one.
Check whether you're signed in with the same Microsoft account that originally stored the photos.
Review the Recycle Bin on both the OneDrive website and your device, as they may not always show the same items.
If the photos still can't be found and the Restore your OneDrive feature is failing after identity verification, it may require Microsoft Support to investigate the account, as they can check whether files were moved, synchronized incorrectly, or are still recoverable from the service.