Mia made the bombshell claim in a recent Vanity Fair interview, stating her ex-husband Frank -- and not her ex-boyfriend Woody Allen -- may "possibly" have fathered Ronan.
"I can't hardly believe that," Barbara told The Desert Sun Wednesday. "It's just a bunch of junk. There's always junk written -- lies that aren't true."
She added that Ronan, 25, was not named in Frank's estate.
Barbara was Sinatra's fourth and final wife. They were married for 22 years until he died in 1998 at the age of 82, UsMagazine.com noted.
Mia was married to Sinatra from 1966 to 1968, but she told Vanity Fair they "never really split up."
She was romantically involved, though never married to Allen, from 1980 to 1992. The relationship ended when Mia discovered Allen was having sex with her adopted daughter Soon-Yi Previn, whom he later married.
Notable deaths of 2014 [PHOTOS]