Ex-MLB Star Andruw Jones -- Fighting Wife for Custody ... I'm the Better Parent

New York Yankees slugger Andruw Jones is battling his estranged wife for custody of their son -- claiming he's the better parent ... just two months after he was popped for domestic violence.

Nicole Jones filed for divorce from Andruw back in January -- one week after the MLB star was arrested for allegedly dragging her through the garage and choking her. Charges are pending.

In the divorce docs, Nicole -- who was married to Jones for 10 years -- asked for primary physical custody of their 9-year-old son AND to have the prenup voided.

Now, Andruw has fired back in his own docs ... claiming HE should get primary physical custody, and not only that ... he shouldn't have to pony up a dime in child support.