LeSean McCoy's Baby Mama Says NFLer Pressured Her to Cover Up Role in Home Invasion

2:22 PM PT -- LeSean just replied to the docs, saying, "The allegations made against me today regarding my relationship with my son are provably false, outrageously inaccurate and offensive. I have a loving and close knit relationship with my son."

He continues, "The young boy is my whole life. With a custody case coming in November, I can see why these false allegations are surfacing."

LeSean McCoy's baby mama claims the NFL star used their son as a pawn in order to vouch for his character, so she would shoot down rumors he was involved in a home invasion that left another one of McCoy's baby mamas brutally beaten.

You'll recall, McCoy's home was hit in a home invasion back in July that left ex-GF Delicia Cordon almost unrecognizable because she was so badly beaten. Cordon and others insinuated McCoy may have orchestrated the attack because he allegedly wanted Cordon out of the house. Cordon has since filed a lawsuit against LeSean.

On Tuesday, McCoy's baby mama -- Stephanie Maisonet -- filed new docs in the Cordon lawsuit.

Maisonet claims the day before the home invasion, she overheard LeSean on the phone saying, "I need to get this bitch out of my house."

Maisonet says after the attack on Cordon, LeSean called her -- something he didn't often do -- and offered her a deal. Maisonet claims McCoy told her if she'd publicly support his character and insinuate he wasn't behind the attack, he'd roll over in their custody case with their 6-year-old son ... and let her enroll the child in school in Miami.

Maisonet says she allowed a friend of McCoy's to access her Instagram account and post a positive message about the NFLer.

In the docs -- obtained by TMZ Sports -- Maisonet says she believes LeSean has abused their son on multiple occasions ... even making a report with child services. She concludes, "I regret ever agreeing to help LeSean McCoy in this case ... I feel like I am sending our son to a monster every two weeks."

She also included a photo of their son, showing alleged bruises from LeSean on his face.