Pittsburgh Steelers wide receiver Antonio Brown ran off with his child and is refusing to give the kid back to his mother ... so says Antonio's baby mama -- but the NFL player claims she's flat out LYING in a soulless scheme to make a quick buck. 

Shameika Brailsford filed docs in Miami, claiming Antonio has had custody of their 4-year-old son in Pennsylvania for months, while he plays with the Steelers -- and she's worried to death he's not being taken care of.

Shameika says 23-year-old Antonio took the child -- also named Antonio -- without her permission, and she hasn't had contact with the kid since Antonio took him away.

Now, Shameika's asking the court for an emergency child pick-up order -- which would require law enforcement to pick up her child and bring him back to her in Florida ... asap.

But Antonio's lawyer Jason Marks says Shameika is lying through her teeth -- telling us, "None of that is true. The mother consented to the child living with Mr. Brown back in February."

The lawyer adds, "The mother obviously knew where the child was the entire time and, in fact, Mr. Brown recently arranged for the mother to visit with the child in Pittsburgh. This is nothing more than a classic attempt to shake down a professional athlete for money."

A judge is expected to rule on Shameika's request in the near future.