When printed by any device a photo has a random and unique serial number printed on an edge of the back,
Every device that can print a photo has a random and unique serial number on it. Maybe only visible in the settings or something so not
If you have a photo, a device capable of printing a photo and a tools, you can use forensics to try and see if that photo was printed by that device. It's not something just anyone can check like a matching serial number. It's something only a skilled forensics expert using the tool can see.
To give it weight, maybe have the tool print a report saying that is is confirmed. Like a report saying that it has been verified by the ForensiToolMatcher3000 that photo number SERIALNUMBER was printed by device SERIALNUMBER.