Separated Parents, Who Will/can/should Claim Our Child ??

Location: Oklahoma, USA *also posted in r/tax
Our child lives with me 6 days out of the week. His father picks him up Sundat afternoon and brings him home Monday morning. We do not have a formal child support/custody agreement through the courts but he does send $300 bi-weekly ($300 = 1/2 My gross income on my weekly check). Tonight his father asked to alternate claiming him bc he winds up having to pay back in every year, instead of getting a refund. At first I conceded but after talking to my boyfriend and mother, I feel like I rushed into the agreement. I do not mind sharing him as a dependent but I don't want to be getting screwed over.. My ex says that he would give me the CTC each year he claims and, to my ignorant brain, that feels fair but when I think about the fact that he sees our boy 50~days/yr or so (not including holidays), I feel like it's uneven but I DON'T KNOW.
So I am asking reddit for some unbiased, and hopefully educated, advice.
P.S. idk if it's relevant but we are very amicable, I would venture to call my ex one of my closest friends. Also, I make about $14-15/hrs while my ex makes $26+/hr with overtime. We have a very open communication with our son but when it comes to things like this, he shuts down. So I just want opinions, advice, whatever.
Also, edit to add: we were never married.
Thank you!
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