My wife want to give birth our baby in USA, if we do that can we get US citizenship or green card to stay and live in US with our son?

Giving birth to a child in the United States provides you with no basis to pursue citizenship or a green card. Your child could only petition for you to receive a green card after he has reached the age of 21. There are no interim benefits that allow you to have status while waiting for him to reach 21. In addition, if you and your wife rely on Medicaid or other public assistance to pay for the birth of your child, you will likely face difficultly entering the U.S. in the future or obtaining a visa.