Ex wants first daughter but not the second

My ex and I have a 4 year old daughter together, and a 3 week old daughter as well. We are not together because I found out he had been cheating on me since before I got pregnant with our second daughter. He did not sign the birth certificate for our second daughter. He did not want to. He had nothing to do with the pregnancy and has nothing to do with her now that she is born. He still asks about our first daughter and for pictures of her, but should I keep sending them or answer at all? He usually sees her once a month. The last time he came to pick her up he didnt acknowledge the baby or ask about her at all. I breastfeed so it would be hard for me to send the baby with him right now, but when she starts to get older I don't feel like its fair for him to take our 4 year old, but not our newborn. I am applying for child support. He pays the bills still, but he he told me that the bills at his gfs apartment went up $500 and I will need to get a job. I already planned to get a job anyways. Im just trying to.figure out whatis best to do by my daughters..