Quincy Jones III plans to serve as the executor of his late father's estate, according to a new court document ... this after his sister Rashida and his uncle Richard Jones turned it down. According to Friday's filing, Jones named Richard Jones as his first choice of executor ... but Richard decided he didn't want to do it. His second choice was with either Quincy III or Rashida ... and, ultimately, Quincy III stepped up while Rashida stepped back. The next hearing date is scheduled for May 11.