Rapper Future -- Baby Mama Deserves No More Cash

Not only does rapper Future want a judge to keep his child support payments in the present and shoot down his baby mama's request for more cash ... he wants MORE custody of his son, TMZ has learned.

As TMZ first reported, Future (real name Nayvadius Cash) and baby mama Jessica Smith hammered out a child support agreement after a DNA test proved Future was the daddy of Smith's 10-year-old boy. But Smith came back a short while later demanding more money because she felt Future lied about how much money he makes.

But in court docs filed last month in Georgia, Future says he financials are all on the up and up and Smith should not receive a penny more in support. He claims that Smith's attempt to use comments he's made in the press -- specifically the one where he claims he always has $25,000 on him at all times -- can't be used as part of the custody battle.

In addition to blocking Smith's play for more money, Future is now angling for more custody. He claims Smith took their son out of school (after Future paid non-refundable tuition) without his permission and has "failed to deliver the minor child to school for unreasonable periods of time and/or delivered the child to school in tardy fashion."

Future is seeking joint physical custody and wants Smith to pay his attorney's fees.