Can I erase the fraud claim on me?

I worked as a teller at a bank. After I completed my training and got the cash box I had outages. Than during one day a customer came back saying that I shorted him hundred dollars and when my drawer was checked my bundles of fifty and 20 were short a few dollars. When asked I told I wasnt aware how it happened. Since I was just starting could be an error since it happens with all the tellers. An investigation was done and it wasn’t proved that I stole it or whatever. I was later terminated because of it and I recently applied again for a job and in the background it came that the bank has placed an internal fraud act on me. I want to ask that if that’s ok or legal as nothing was proved and there was no evidence . Should i file a case against them. I would also like to add that when they fired me I was said I am fired for force balancing