Has anyone ever done the paternity test you take while pregnant? I had an acquaintance tell me years…

Has anyone ever done the paternity test you take while pregnant? I had an acquaintance tell me years ago she had one done and it was $2000. I know who my baby's father is but because of some bullshit drama he and his mother are demanding a paternity test. I told him about what the woman told me years ago and how it's cheaper to do it after the baby is born but doing it after the baby is born means he has no rights until he proves paternity and the baby will have my last name. He said the would rather wait till after because it's cheaper. But then his mom texted me saying the baby should have his last name and I told her he will have no rights until he proves paternity and won't be on the birth certificate and she thinks she found a way to do it cheaper. I googled it and found a test for about $60 but I'm pretty sure there is a cost to send it in and get the results. Which I think could be the $2000. And i know I could put him on the birth certificate without a paternity test but because of the way of his lack of responsibility and general negativity I get when even talking to him I don't plan to let him be there for the birth. Don't judge or bash me for that cause I have plenty of sound reason for that. But since he wants a paternity test on top of all the hell he has put me through I'm not putting him on the birth certificate until I have to. So far i do not believe he would be good for this baby.