Managing Project and Contract Management

it is a fixed price contract, but they are insisting that there are some activities they are doing or they did before which was not part of this contract.

As a contractor many moons ago my response to clients that advised me there was no additional moneys (no appetite for change orders) was: "then don't ask me to do work that is over and above the initial scope. You, as the client, are the only ones that can control scope growth which invariably results in additional expenditures, extension in contract duration and billings."
Yes, you could be stuck with a unethical contractor, however the most likely scenario is that the client has/had an active role in the current situation. Look inward as well as outward.