Pauly D & Baby Mama -- CUSTODY WAR ... They Hate Each Other

Pauly D and his baby mama are at war, TMZ has learned ... and there's a big fight over custody and cash.

Sources connected to the baby mama and baby daddy tell TMZ ... Pauly doesn't think the woman is a fit mother -- he points to the fact that she once worked at Hooters. He's also concerned because the woman, who's only 25 years old, has another kid.

Pauly and the woman, who goes by Amanda, have filed dueling court docs. We're told Pauly wants some sort of custody of his daughter -- but the level of custody is unclear. Sources say Pauly has not seen the child, who was born in May, but obviously he's looking to change that.

We're also told the baby mama is demanding child support ... and even though Pauly says he's ready and willing to step up and take care of the kid financially ... he feels like she's treating the kid like a winning lottery ticket. Exhibit A ... the woman recently posed the baby in a high chair that's covered in $100 bills.

As for how they hooked up, we're told it was one drunken night in Vegas ... but the kid isn't bringing them any closer. In fact, one source tells us they straight up hate each other.