The woman who claims Justin Bieber fathered her child -- originally accused her ex-boyfriend of being the daddy to the very same baby last year ... this according to her ex-BF's grandmother.

TMZ spoke with Frances Lippe ... who tells us Mariah Yeater had been dating her grandson John Terranova in Las Vegas toward the end of high school.

Lippe says Yeater came to their home in December 2010 and told Terranova she was pregnant with his child. He insisted he did not get her pregnant.

The two got into an argument and police were called ... because Yeater allegedly broke a car window out of rage.

Later that day, according to the police report, Yeater returned to the home to work out a payment plan for the window ... and got into another altercation with Terranova ... and allegedly slapped John 3 separate times in the face with her open right hand.

Yeater was arrested and charged for battery. A court date has been set in Vegas.

Lippe tells us they never heard from Yeater again after the December altercation. 10 months later, Mariah surfaced ... now claiming Bieber is the father. JB says it just ain't true.

Mariah gave birth to a baby boy in San Diego on July 6 -- she did not list a father on the birth certificate.

We've made multiple calls to Yeater's attorneys -- so far, no response.