Legal Question in Civil Litigation in California

It doesn't work that way. Exemplary damages mean the same thing as punitive damages. Those are damages awarded to a party who files an adversary claim and proves to the trier of fact that they are entitled to them pursuant to Civil Code section 3294.

I agree with Mr. Roach. A plaintiff who wants exemplary (aka punitive) damages must ask for them in her complaint. Such damages would then be awarded or denied as part of the judgment. If there is already a judgment in your favor, then it is too late to seek punitives.

There are some unusual circumstances in which this general rule might not apply. You should consult with a lawyer about the specifics of your case to see if any such circumstances are present.

As the defendant you are not entitled to any kind of damages, exemplary or otherwise, unless you filed a cross-complaint back against the plaintiff at the time you filed your answer, or after that with leave of court, but certainly well before the case went to judgment. It is WAY too late now.

I believe the above tells the story. You may want to discuss with your attorney the possibility that you may have a malicious prosecution claim.