First of all, I am not aware that Jasper Tudor had an illegitimate son, nor have I seen any documented evidence that such a son existed. Jasper did have at least one illegitimate daughter, Helen (or Ellen) Tudor, wife of William Gardiner (a cloth merchant) .. and is thought to have had a second illegitimate daughter named Joan Tudor, the supposed wife of William ap Yevan.
The sons of these daughters are a matter of debate. Helen Tudor is thought by some to have been the mother of Stephen Gardiner, Bishop of Winchester. She is known to have had at least three sons, but it is not at all certain that the Bishop can be attributed as her son.. it appears she did, though, have a son named Stephen.
Joan Tudor is thought to have been the mother of Morgan ap Williams, whose wife was Catherine Cromwell, and whose descendant is Oliver Cromwell, the Lord Protector.
As far as I know, these are the only children attributed to Jasper Tudor. He had no children with his wife, Catherine Wydeville. Her five children were Staffords - by her first husband, Henry, Duke of Buckingham, and these appear to be her only children as she had none with Jasper Tudor or with her third husband Richard Wingfield.
There is a reputable family tree for the descendants of Sir Roland de Velville. Sources are cited in the endnotes section. These are the descendants of Jane Velville, who married Tudur ap Robert Vychan. It is through their daughter, Katheryn of Berain, that the family descends.. she was their only surviving child and sole heiress of her father and apparently of her grandfather, Roland.
Incidentally, Katheryn's Tudor
(anglicized) surname was only derived from the fact that her father's first name was Tudur. In the Welsh tradition, she was
Katheryn ferch Tudur ap Robert Vychan. She was still related to the Tudor kings, however, through both her grandfather Roland de Velville and his wife, Agnes Griffith.. her grandmother's lineage was legitimate.
Certainly no supposed son of Jasper Tudor could have been a grandparent of Katheryn of Berain. That is simply and absolutely wrong. Obviously his son could not be Roland de Velville, and Katheryn's paternal grandfather was a Welshman named Robert Vychan, as evident by the name of her father.
Jane de Velville appears to be the only one of Roland's two daughters that had issue. The other daughter, Grace, appears to have either died young, unmarried or without issue, as I have only seen her name mentioned in passing.
Roland de Velville had no sons, or at least no sons that survived to adulthood, and this is evident by his will in which he left all his chattels to his wife. His daughters are not mentioned in the will.
You can find the tree here
A Richer Dust - The Descent of Hughes
The tree goes backwards, so check out page four first and then page three.