I have to sign this 37 CFR 1.63 and acknowledge I am the inventor?
I doubt anyone can force you to sign anything. The question really is why wouldn't you want to. If you are the inventor why not take some credit? I suppose you could be trying to punish you old company, but having a patent on your resume is a plus. If they are willing to foot the bill to obtain a patent, I can't see any reason not to sign.
Do I own any right ? (I do not on the first patents that were filed on this invention, they were made during the course of my employment).
It probably depends on what your agreement was with the company when you were an employee. Most likely you signed an agreement assigning ownership of your inventions to your company as a condition of employment. This is pretty standard and understandable since you are being paid to do the work. In that case, the company would own it. Many companies provide some monetary incentives to inventors. If this were the case when you were an employee, then I'd certainly expect and would request you get it now if the patent is granted.
What if I'm trying to get back at my previous employer?
You didn't ask this question, but from your comments it seems you have an axe to grind with your previous employer. In that case what I might suggest is you tell them that you would be happy to sign, but not until you review the patent application for correctness. After all, your name is on the application as an inventor, you should want it to be correct. As an inventor you are uniquely qualified for the task. And, by the way, your fee for this task is 200 euros/hour (or whatever you feel is justified).
I'm answering as an inventor who has had patents issued since leaving a company. I am not an attorney so please don't take this as legal advice.
