This keeps coming up, and keeps having to be shot down. Sir Richard Yorke's parentage is obscure, and his career seems to be centered on the City of York: "The elder Sir Richard York (d. 1498), founder of the family, and great-grandfather of Sir John York, was admitted to the freedom of the city of York by purchase in 1456. In 1459 he was chamberlain; in 1466 sheriff and mayor of the staple of Calais at York; and in 1469 and 1482 he was mayor of York." https://en.wikisource.org/wiki/York,_John_(DNB00)
Despite being Duke *of* York, Richard Plantagenet spent very little if any time *in* York. His main residence was Fotheringhay, in Northamptonshire, but he could be found all over southern England, wherever Court business took him. He also spent several years on campaign in France, and had a year or so of trying to deal with the Irish from Dublin.
In short, there is no evidence that the two men had any relationship whatsoever. (And while the Duke had a son Richard, he most certainly was *not* Sir Richard Yorke - oh no, he was Richard Duke of Gloucester and King Richard III!)