Vassal Benford, chairman of B.B. King's estate, tells TMZ ... the family is super unhappy with what they say are outlandish inaccuracies in a new, unauthorized biography written by Daniel de Visé's and dubbed "King of the Blues: The Rise and Reign of BB King." It drops Oct. 5.

The Pulitzer Prize-winning author writes ... King's 15 children with 15 different women can't be biologically his because the guitarist was sterile due to an accident as a kid and an illness.

The author claims loved ones -- and even King's doctor -- told him they didn't believe King had biological children. The author also points to King's accident when he was 12 ... after a ram's horn smashed his testicles. The author claims there was no doctor around so "the mangled organs were left to mend on their own."

As for the illness ... the author claims he was told King's testicles suffered further damage caused by a sexually transmitted disease contracted in his late teens.

Benford, however, tells us he spoke to 3 of B.B.'s children ... all of whom feel the accusations in the book are inaccurate and offensive. After speaking with the children, Benford says they told him King was NOT sterile in the 1950s ... when he had most of his children. He married twice but didn't father any children with the 2 wives.

Benford told us several of B.B.'s kids are definitely biologically connected to him, but when asked to clarify how many of the kids were biologically B.B.'s children he declined to answer.

Nevertheless ... we're told B.B., who died at 89 in 2015, considered all 15 of the kids as HIS ... regardless of biological connection. Benford says he loved them deeply.

For its part ... Benford says the estate's developing a biopic that'll portray an accurate depiction of B.B.'s life and the relationship with his 15 children. It's expected to drop in 2022.