Final pay/ quit claim

Is it legal to not release the quit claim if an employee did not render 30 days of service? I was able to ask all my superiors the approval of my situation where in I cannot render the needed 30 days of service upon submission of resignation letter. I also had a talked with the manager regarding this. My resignation was approved but they want me to render the 30 days, but I told them that I cant because I have to start to my new work. Please advise. I already had my clearance and yet the manager in HR said that she cannot sign it due to the rule of 30 days service. Its been 1 month and I'm thinking if they're gonna give me my quit claim.

Well, without the required 30-day notice, you may be liable for damages.