Two new potential Prince heirs are stepping forward to get a piece of the pie..

According to docs filed in probate court...Norman Yates Carthens says Prince adopted him -- he's not specific about when -- and claims there IS a will that...left him $7 million. He makes no mention of where this mysterious will is right now...

Also, an alleged half-sibling named Regina Sorenson filed docs saying she and Prince had the same father. In the docs she says there is a trust, and she should be included in any DNA testing of potential heirs.

TMZ: Claire Elisabeth Elliott filed a request for the court to remove Bremer Trust bank as administrator of Prince's estate, because she believes she should be calling the shots as his "Sole Heir."

Claire even claims there is a marriage certificate and will to back her up. It's worth noting she did not attach those documents in her filing...(W)e checked Minnesota court records -- no dice.

Claire also filed docs to run for President of the United States...