Can an adverb precede modal verb? I've seen this kind of sentence: I just can't believe what happened
Yes, it's a grammatically correct construction.
The problem is that semantically it rarely makes sense (verbs like can, should, etc. don't really have any qualities that could be modified by an adverb), and the only example I can think of is using it for added emphasis:
I simply can't understand why you did it.
I really shouldn't have done that.