Hi Norton-
I also descend from Robert Stewart, but via his granddaughter Deborah, so a female line. There are several men who descend on the male line who are testing YDNA with FamilyTreeDNA's 781 and Royal Stewart (Stuart) projects.
Here is some information that one male line descendant has found. https://hereldstuart.wixsite.com/stuartfamily/about-robert
As far as I know, the idea that Robert descends from Francis and his father, Francis the 5th Earl of Bothwell, seems to come from a hypothesis first made in the Clan Stewart magazine in the 1920s. There is also something about him having a son named Robert and or a brother listed in Wikipedia.
This is the paragraph often cited: 'His eldest son, generally called Charles (b. 1617), fought in the Civil War, but is said to have died in England after the Battle of Worcester in 1651,[45] and on 26 November 1656, his brother Robert was cited as the heir to their father's debts when the barony of Coldingham was acquired by the Home of Renton family.[46] He appears to have died without issue, and their unmarried sister was regarded as the last of the line.[47][48]
There is no birth record. I believe Francis, the son of Francis 5th Earl, went to Ireland.
We are finding DNA connections to an Alexander Stewart of Ballymena, Ireland.
Please consider joining the FTDNA projects to help the research - your male line DNA is incredibly valuable.
Francis, Lord Stewart and Bothwell, and his wife Isobel Setoun are reported to have had a son named Robert, but evidence to prove that it was this Robert Stewart who settled at Norwalk in Connecticut has not so far been produced. In the absence of evidence he should be disconnected from the family tree of Lord Stewart and Bothwell.
https://archive.org/details/scotspeeragefoun02pauluoft/page/172/mod...
Robert Stewart who married Bethia Stewart could not have been the son of Francis Stewart, Lord Stewart and Bothwell - he’s not the same as Robert Stewart who is noted as resident in Scotland in 1658. Robert of Norwalk is thought to have arrived to Boston in 1652.