I'm going to presume that is what you're saying here. Do you have an attorney? You might want to consider bringing an attorney with you to court. I would strongly advise it.
So she had the child, and she's not willing to put the child up for adoption?
There are no hard and fast rules about how to get out of paying child support. Most courts don't allow you to terminate your rights just to avoid child support, but maybe new law needs to be made. If you can show that she tricked you into getting pregnant, you may have an easier time, but you will have to show that you did something to prevent the pregnancy also, which you can't show if it was unprotected sex. You took her word for it and she lied. And lied.
I'm really sorry about this.This is not a good way to find out she's been lying to you.
One way you can try to get out of this is to be honest with the court, tell the court she tricked you into it and explain what great lengths she went to to deceive you, and how she deceived you.
The issue of terminating parental rights in California often comes up as part of an adoption process. For example, in a stepparent adoption (if she were to marry someone else), the biological father (you) can consent to the adoption and voluntarily waive your parental rights. It would have to be a stepparent adoption and then you would be able to terminate your rights.
So,she would have to serve you with father with notice; you can waive further notice or, if you do not file a paternity action within 30 days, your rights can be terminated, often without a hearing in California.
Other than that, there are really no guidelines for terminating your parental rights.
In some extreme cases, a judge may side with you and decide that you were tricked into this so you shouldn't have to pay child support, but this is rare and there really isn't legal precedent for this in Cal at this time, so you'd have to make new case law. Seriously, making new case law has been done. One of my cases made new case law in my state. Occasionally that happens.
Other than that, I strongly suggest you get a lawyer and fight this tooth and nail.
I don’t always say to get a lawyer, but in this instance I would. We aren't allowed to refer to any particular lawyer. However, what I do here, which helps my customers tremendously, is I give you a list of lawyers in your area and I'll show you how easy it is to pick one.
I have a short, easy to understand free guide and it will show you what to look for in an attorney. You can always run your picks by me and I can let you know if I think you're on the right track. I will also look for LegalAid and pro bono attorneys in your area if you tell me to do that. I just need to know where to look. The bigger the city the better. My customers tell me they have found great lawyers from my information. This part is free of charge -- I do this as a courtesy to my customers here. Just let me know if you want this information.