Paternity leave issues?!

So I’m 34 weeks pregnant and my boyfriend is trying to get paternity leave. He’s been working for his company since October of 2018, so not a year yet. His boss has been telling him that all he has to do is call HR and get the leave info, so that’s what he did. Now HR is saying that he doesn’t qualify at all, even for an unpaid leave-because he hasn’t worked there for a year. My boyfriend tried to ask if he takes more shifts if they’d let him, and they said no. Is there anyway he can get any kind of paternity leave from the state or even fight this? I’m going to be a first time mom and have no one at all to help me besides him.