Sources close to "X-Factor" tell TMZ ... Sophie Simmons showed up at the San Francisco auditions yesterday ... saying she wanted a "fair shot" and telling the judges, "This isn't about my dad. This is about my audition."

Of course ... her famous father was in attendance, but we're told he almost didn't make it. Sources say the KISS front man got a surprise call from his 19-year-old daughter the night before ... saying she couldn't come home for Father's Day because she was trying her hand at the talent competition.

We're told Gene decided to hop on a private jet and made it just in time to see his daughter belt out some tunes.