Adrian Peterson fathered a 4th child, his 2nd secret child, and the mother was a waitress at a popular Twin Cities nightclub, TMZ has learned.

This has been confirmed by multiple sources ... the child is a 3-month-old little girl who's living with her mom in Minnesota.

Sources close to the situation tell us the child's last name on her birth certificate is listed as "Peterson."

On the day Peterson's 2-year-old son Ty passed away, the mother of AP's 4th child posted an emotional message on her Facebook page about the situation.

"Today has been a long day finding out my [daughter's] brother passed away and knowing that she never even got to meet him."

Read more at TMZ HERE