Disputed Parents
There is a internet fantasy claiming that William Smythe of Hatfield, Yorkshire, England was the son of Richard Smythe and wife Alice. There is no known evidence to support this supposition. According to the two journal articles cited below claimed to be the current state of research on this topic by the General Society of Mayflower Descendants as of 2014[1] his parents are unknown.[2][3]

Disputed Wives
According to the two journal articles cited below claimed to be the current state of research on this topic by the General Society of Mayflower Descendants as of 2014[1] William Smythe of Hatfield, Yorkshire, England had one known wife: Catherine and he had one unknown wife. There is no evidence that he had a wife named Agnes Simkinson, Joan Allen or Cynthia Rawls (findagrave.com)