Prince's siblings say a woman and girl purported to be the singer's niece and grandniece have no genetic connection to Prince and should not be named as heirs to his estate.
Attorneys for Prince's siblings and half-siblings argued in documents made public on Tuesday that Brianna Nelson and Victoria Nelson aren't Prince's heirs as a matter of law, and a judge should deny their claims.
Potential hearings have been set for November.
Prince died on April 21 of a fentanyl overdose, leaving no known will.
Brianna and her niece, Victoria, claim they descend from the late Duane Nelson Sr, who they say was Prince's half-brother. They don't claim a genetic link, but say Prince's biological father held Duane out as his son.
Prince's siblings say that isn't enough to prove heirship.
As it stands now, Prince's sister, Tyka Nelson, and his five half-siblings are in line to split Prince's estate six ways.
Should the court count Duane Nelson as another half-sibling, Brianna and Victoria -- as well as possibly a man who recently claimed to be Duane's son -- would be entitled to one-seventh of the estate, which has been estimated at between $100 million and $300 million in total.
Carver County District Judge Kevin Eide has already found that Brianna and Victoria have presented a plausible enough case to proceed and don't need to undergo genetic testing.