How do we get rid of the ex-girlfriend?

I've fallen in love with this great guy who got out of a bad relationship. She was pregnant when they broke up and he wanted to take responsibility of his child but now he's finding out dirty secrets of hers. She cheated on him while he was at work at least 3 times and one of those times was with 2 guys at a time. Now he wonders if the baby is his. The baby was born almost a week ago but it was born premature. We can't tell if the baby looks like him yet and she's such a liar. She's been texting him saying that he's going to pay child support and that he's not going to see the baby because she "knows" that we are doing meth. Ha! We'll both take hair follicle tests. He hasn't answered her calls or responded to her texts since the day they split but she won't stop calling and texting. He changed his number yesterday. He wants to do the paternity test but doesn't know how to go about it. We don't have the money to pay for it. What is the best way to handle this situation?