Yes, it is possible to get a paternity test during your preganncy. However, most people will do it after the child is born, it is easier to extract the DNA.
Your baby would get the DNA test for paternity after it is born. If you are at risk for a genetic defect, then your doctor would discuss that with you during your pregnancy.
see link below
Once paternity is established, payment of pregnancy expenses is often ordered.
Starting 10 weeks into the pregnancy. see related question
Child support does not begin until the child is born and paternity is established. In Kansas, support has to begin during the pregnancy.
see link below "Can you have a paternity test while you are pregnant?"
Yes, a paternity test can be conducted both before and after pregnancy and will involve one of several different procedural options for each.
A DNA paternity test can be done shortly after birth, a sample is gently taken in from the baby's mouth. The test can be done during pregnancy via amniocentesis or chorionic villus sampling but most doctors won't perform these tests without medical necessity due to the chance of miscarriage.
It will have to be determined through a paternity test if the father is denying the child. If the father admits the child is his, no paternity test has to be completed.
Though as yet, this is not illegal, there's a growing push to establish penalties for paternity fraud. If she's not agreeable to it, you need to file a motion to force a paternity test, which can be done during the pregnancy. This is particularly important in Kansas where you're obligated to begin providing support during the pregnancy. see links Under limited circumstances, you can even file for custody, now. see links
during pregnancy-no during labor yes