Louis Tomlinson: Custody Fight ... Baby Mama Won't Let Me See My Kid

Louis Tomlinson has lawyered up to wage a custody war, because he says his baby mama is not letting him see their kid ... TMZ has learned.

Sources connected with Louis tell TMZ, the One Direction singer claims Briana Jungwirth has gotten greedy and wants money ... and lots of it. He claims she's using their 1-month-old son, Freddie Reign, to leverage a bigger payday.

It's a surprising turn ... Louis got Briana a 3 bedroom home in Calabasas and he's renting a $21 million home in L.A. to be close to Freddie.

Louis has not gotten a DNA test but says there's no doubt he's the dad ... they dated exclusively during the period in which she got pregnant.

We're told Louis is gunning for an order forcing Briana to give him some custodial rights, including significant access to his son.