Get back the data lost from the restoration?

I was using a peripheral storage device as duplicate data for a particular network storage link. Not long ago my computer system started to not recognize the integration and as a result, I tried to switch my network storage for another one. To make it functional, I had to restore my peripheral storage’s system; midway.
I realized that I was not able to duplicate some of the first files but the system had already started removing some files when I terminated the process. I would like to know if there is any way I can get back the data lost from the restoration?
