O.J. SIMPSON’s daughter Sydney is sick and tired of hearing incredible reports that KHLOE Kardashian could be her half sister, say sources.

As The ENQUIRER reported a year ago, O.J. – who’s locked away in a Nevada prison – has been crack­ing jokes that Khloe, 28, could be his daughter from an affair he had with Kris Jenner while she was married to his close pal Robert Kardashian. In a follow-up story in September, we reported insiders saying that O.J. told pals he was consid­ering writing Khloe into his will.

And that, say sources, is what sent Sydney over the edge. Although O.J. is serving a 33-year sentence for armed robbery, he continues to accrue a $300,000-a-year pension from the National Football League and is said to have as much as another million stashed away in the Cayman Islands.

“Sydney says she is  sick and tired of hearing that Khloe could be her half sister,” said the source. “It blows her mind even more that O.J. talked about putting Khloe in his will.

“Sydney told a pal, ‘It’s just so un­fair. Khloe already has everything in the world at her fingertips.’”

A family insider added that the 27-year-old is “heartsick” over O.J. embracing Khloe so publicly.

“Sydney despises the whole Kar­dashian clan, especially Khloe,” revealed the insider. “She resents the glamour and fame that Khloe and her sisters bask in. Sydney feels that ever since her mother’s murder, she’s had to bear the stigma of being the child of a killer.

“It galls her that the Kardashians are rich, pampered TV stars while she’s had to work for everything she’s ever gotten.

“Sydney says, ‘Khloe makes me sick!’”

O.J. was acquitted of the 1994 murders of Sydney’s mother, Ni­cole Brown, and her friend Ron Goldman. Before their split, O.J. and Nicole had enjoyed a close friendship with Robert and Kris Kar­dashian. O.J. had even served as an usher at their 1978 wedding.

Kris and Robert had four kids – Khloe, Kim, Kourtney and Rob­ert Jr. – before divorcing in 1989. Kris married Bruce Jenner shortly after, and they had two daughters, Kendall and Kylie.

Ironically, it was Khloe who first brought the pater­nity question to the forefront when she jokingly quipped on TV that she wasn’t “a real Kardashian” because she doesn’t resemble her sisters Kim and Kourtney. She does, however, bear a striking resemblance to Sydney!

For her part, Khloe remains tight-lipped about her re­lationship with the Simpson family, and the other Kardashians have de­nied that O.J. is Khloe’s father.

But that’s little consolation to Sydney.

“Right now Sydney is beside herself,” said the insider. “All these years she’s had tremendous feelings of conflict over her mother’s tragic death and her father’s role in her murder.

“Now O.J could betray her again if he actually accepts Khloe as his daughter. Sydney’s heart would be shattered.”