Richard III had one legitimate child, Edward of Middleham, died at the age of 11 years or under. He had two acknowledged illegitimate children: Katherine and John. Katherine was married in 1484 to William Herbert, Earl of Huntington, and died before 25 November 1487. There is no record of any children, her husband died 1490 without a son. John of Gloucester (b circa 1470) was granted an annuity during the first year of Henry VII and was later imprisoned. He is probably the bastard of Richard III that Henry had quietly murdered in 1499. He never married and there is no record of children. There is a story that the night before Bosworth Field Richard III told one Richard (1469-22 Dec 1550) he would be acknowledged as his son if the king won the upcoming battle. The boy became a bricklayer in Eastwell, Kent. He might have had children and could conceivably have descendants living today, but I doubt you could prove anything.