The cost of a CVS (chorionic villus sampling)done for paternity purposes will be very expensive, no matter where you live. Not to mention, it can be hazardous to your pregnancy.
CVS is usually only done to determine the risk of genetic issues in the embryo (or very young fetus) and that is covered by most insurance. But it is not commonly done to determine paternity.
You would have to contact local OB/GYN clinics around your area to find out if they know any perinatologists (specialist doctors who look after high risk pregnancies and perform high-risk procedures) that perform CVS tests and if they will run the tests to determine paternity.
Chances are you will have to wait until after the birth to determine paternity.
By the way, you need to get out of the violent relationship you are in. Don't stay for your son. Leave for your son, and yourself. Don't have a place to go? There are many women's shelters that will help you out.
Womens Council for Domestic and Family Violence Services may be able to help you out. You can google them. Also, here is their number: (0

9420 7624