Should I let my ex see our son?

I gave birth on the 11th and I haven't even let the baby daddy see him. I haven't even sent a picture or told him his name either. We were living together for 2 years, we planned this baby, he proposed then cheated on me when I was 4 months pregnant. I immediately moved out after finding out and I also discovered a secret Gmail account where he's been emailing multiple women even up to when we were just dating. I'm so hurt by this man. He played me the whole time and I fell for all of it. Am I wrong to keep his child from him? He has only given me $40 during my pregnancy in preparation for our baby but on social media he is out partying and golfing every weekend. He served me with papers for joint custody and visitation the other day. So now it's definite that I have to deal with this person till our kid is 18 😔 am I horrible to withhold information?
Updates:
+1 y
I should add that I moved 150 miles away, and next year I plan on returning to my hometown with my parents to go to college as im struggling to support myself and my 2 kids, that'll put 1,800 miles between us. So I'm not sure how he can be an active part in his life if he's not willing to move from where he is now.
Should I let my ex see our son?
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