Q: Do I have to pay a cancellation fee to an open access journal that wants to publish my paper without peer review?
I submit a paper to an open access journal, and it was accepted and the publication fee EUR2000 was required to pay before I know it. I claimed that it is not fair to publish without a peer review and the author’s consent. But they insisted that they have informed the result of peer review a few times and the publication cannot be cancelled since it is already in press. Actually I was late to find their messages, since they were sent to my spam mail folder. The cancel fee is EUR1500.
From your description, this seems to be a predatory (bogus) journal. Predatory journals typically publish articles without a (proper) peer review. They do not even have (qualified) editors on board. They are typically out to make money by targeting unsuspecting researchers who are under pressure to publish.
You should write to the journal immediately asking them to stop publication. State that you would like to withdraw the article and will not be able to make any payment. They are not likely to agree and will put further pressure on you by saying that they have already processed your article for publishing. In case they go ahead and publish the paper even without receiving payment from you, do not mention this article on your CV. I can understand that it will be a huge loss for you in terms of time and effort, but publishing in a predatory journal can affect your academic credentials. Unfortunately, there's not much you can do if they end up publishing the paper: you will have to take it as a learning experience and be more careful in the future.
For the future, here are some resources to help you identify and avoid publishing in predatory journals:
This content belongs to the Journal submission & peer review Stage