Child Support question

My husband choked me and slammed me into a wall when I was 4 months pregnant and no I didn't provoke him.

He went to jail I had the baby and I put a protection order against him

( I wanted to give him a chance to be a father regardless of what me n him got on on)

Once he got out I let my sister communicate with him about our son with me n the room of course from a wifi number on my phone so I can keep up with what's said

(I do not recieve any government assistance and he is not on the birth certificate)

So fast forward Our son is a year old and he hasn't even brought a dollar pack of wipes ,he's always making broken promises about help and I don't ask for much just 50 a week or 200 a month... that's not even half of the $722 I pay a month

So lets break down $722

His academy/Daycare is $172 a week× 4weeks is $688

Wipes per week is $11×4 is $44

And diapers/pull ups for a month is $40

$688+40+44= $772÷2=$361

But im only asking for $200

My question is can I place him on childsupport and still go after him for full custody?