Im not the father, should i remain friends?

Here's my story. I met a woman about 6 years ago, we went on a few dates. it eventually turned into a friends with benefits situation, which isn't what I wanted so I ended things and moved on. we were still cool, there was no bad feelings or anything, we were "hi/bye" type of friends after that and eventually lost all contact. A year or 2 later, I got into a serious relationship with someone else, was engaged for a while. that relationship lasted 3 years. It ended and I decided I didn't want to jump back into a dating for a while.

2 months after that relationship ended, I joined a dating website. I was only on that dating website for 2 weeks and I deleted my account, decided I wasn't ready. during the 2 weeks I was on the dating website, the first woman from the beginning of this story messaged me from the site as she was also on that site. we met up once for coffee and it turned into a one night stand. I still wasnt ready to date, I never pursued anything else with her or anyone. we remained friends, went back to the "hi/bye" type of friendship we once had.

2 months after our interaction, she contacts me and tell me that she is pregnant and I'm the dad. I had questions because the dates on the sonogram and the time me and this woman was together didn't quite match. which was easy to figure out because it was only the one time. I didn't blow her off, I hung in there with her through the pregnancy, she had the child, we had a paternity test, I'm not the father.

Now. I never believed that she really thought I was the father, she was way too calm and nonchalant about the whole thing. the test results didn't really seem to surprise her at all. she was more worried about me cutting off all contact if I was not the father from the conversations we had before the test. but what is happening now, she is asking for money and rides here and there. this is becoming a once/twice a week thing now. Not a lot of money...$30 here, $40 there. a ride here... a ride there. I have given her the money sometimes, but id say half the time I tell her I don't have it. I hardly ever give her the ride she ask for. She also has her family/friends still thinking i'm the dad. she hasn't told them because she doesn't want to have to deal with critical looks. she does know who the dad might be (I found that out later on) and haven't told him yet either (he lives in a different state)

I'm wondering if I should even continue contact with this person. on one hand, I kindof feel an obligation that frankly I shouldn't, but I don't want to be this persons support system, I have my own life. Was curious as to what you guys think? do i need to cut all contact?