Temporary Assistance in NY

I'm 26 weeks, no job and haven't had luck finding one. My baby's father said he'd be willing to let me live with him if I could help out financially, which is fair, but I can't do it at the moment. I've been staying with my grandma and was looking into temporary assistance and I think it would be a huge help right now. Then I was thinking that maybe if I bring this up to my baby's father, he'd consider letting me live with him so that we can raise our baby together. But what I'm wondering is, could I live with him and still be eligible for it? Since he has a job (a low paying one), would they deny me? Would I have to say that we are living together? And if anyone has temporary assistance, how does it work? Do they give you cash or a card with the money or a check? Could you have food stamps while getting temporary assistance too? I of course don't plan on using and abusing the system and 100% plan on still searching for a job, just right now things are super stressful.