Need Advice, don't know what to do.?

I dated a girl for 1.5 years. I broke up with her, five days later shes announced she was pregnant. I thought she was lying, but she actually is. I expressed how we need to stay friends and be civil for the child's sake, but that I would never get back with her(I broke up with her for lying and not keeping a job..ever). Basically this upset her that I wouldn't get back with her(she is now 6months pregnant) and she has told me that she has had miscarraged, had an abortion due to her having to having to get treatment for cancer(which she also made up..the cancer), her dad had a heart attack and the list kinda goes on but those are the bigger ones. Shes been calling me obsessesivly so i changed my number. The problem is that I want to be part of the childs life(of course) and I'm ready to financially support my child with whatever I can spare, but I don't know if I can raise a child jointly under these conditions, shes making it impossible for me to want to even know her. She has threated to make the kid hate me if I don't, "step up"(is what she says) and be with her. I dont really believe that fighting for custody is an option considering the cost of it not to mention that judges almost always faver women.. so i hear. shes 23 and wasnt crazy like this until about a year after dating. I kinda feel comfortable with just leaving the whole situation and paying child support is that wrong? I just don't know whats best for the child. Mature advice would be appreaciated... thank you