Billie Jean Jackson claims to be secretly married to the reclusive popstar and says she gave birth to Prince Michael II.
She now wants joint custody of the six-year-old and regular visits.
Billie Jean said she filed the suit at LA Superior Court "because she is always arrested at the home of her husband, Michael J Jackson".
She is demanding a payout of around £700 million, visitation rights at weekends and a say in the boy's education, the paper claims.
Jackson has never identified Prince Michael's mother but said he was born to a surrogate using artificial insemination.
It is not the first time he has faced maternity claims.
British woman Nona Paris Lola Jackson has lost several lawsuits since 2006 after claiming to be the mother of all three of his children.
Jackson has 30 days to respond to the lawsuit.
In 2002, Jackson was strongly criticised for dangling the boy, who is nicknamed Blanket, over a hotel balcony while he was showing him off to fans waiting below.Original here