Harris, who died in 2011 after a battle with throat cancer, joined the star's backing band in 1959 when it was known as The Drifters, but quit in 1962 following an alleged affair between his wife, Carol Costa, and Richard.
The musician's son, Ricky, has now spoken out to claim he is the product of the rumoured love affair, and he is demanding the superstar take a paternity test to prove whether his suspicions are true.
Ricky, 53, tells Britain's Mail on Sunday newspaper, "I'm not after anything from Cliff. I don't want his money. I am just trying to find peace of mind. For more than 50 years I have been the man in the middle. All I'm asking is that Cliff takes a Dna test to put my mind at rest once and for all. I plan to begin legal proceedings to start this process and, if I'm wrong, I will apologise to him...
"I have had this thought that Cliff might be my real father for years, but it is only in recent months I decided to do something about it... Jet died in 2011 and we're all getting older. Cliff won't be around for ever. I just want to know if he is my father, as I believe."
A representative for the singer had yet to comment on the claims as Wenn went to press, but Bill Latham, Richard's former agent who retired four years ago, branded the report "nonsense", adding, "Cliff doesn't have a son."