Can you believe I paid exactly zero dollars in child support last year to two of my sons?
That's difficult to believe. Why haven't you paid any child support?
I don't believe that I should have to pay for their care, my ex-wife took all of my money anyway.
If these are your biological children, it's your duty to support them financially. You should try to build a good relationship with your children because you will likely regret not having a relationship with them in the future.
What are they going to do? They weren't even born when I was at my highest earning.
You may not be earning as much money as you were before they were born but as their father you still need to support them. The government will make you pay for their support anyway so why not agree to provide care for them now before you get into trouble?