To back up their claims as rightful heirs, the girl's lawyer said that Fischer had sent the family considerable amounts of money on eight separate occasions, along with postcards signed "Daddy".
The reclusive chess mater's estate is being contested by Miyoko Watai, a Japanese chess official who claims to be his former wife, along with two American nephews and the US government, which is seeking unpaid tax money.
Under Icelandic law, a woman who is a lawful wife is eligible for a third of a deceased person's estate, while a child inherits the remaining two thirds.
Fischer, a child prodigy, was the world's youngest chess champion.
Fisher started playing chess at age six and won the US adult championship at 14.
He won the US title in 1964 with a score of 11-0, the only perfect score-line in the tournament's history. He spent 54 months as the world's number one player.
"Chess is war on the board," Fischer once said. "The object is to crush the other man's mind."
Fischer became a Cold War hero in the US after he defeated Russia's Boris Spassky in a 1972 chess game.
However, he fell out of favour with US authorities by playing a rematch with Spassky in Yugoslavia in 1992 by defying sanctions and was threatened with a 10-year jail term if he ever returned to the US.
He renounced his US citizenship and reportedly said, "I want to see the US wiped out" after the 9/11 attacks.