Alexander Stewart was born about May 1786 to Archibald Stewart and Mary McLean in Campbeltown, Argyll and Bute, Scotland. Later in life he married Katherine Kelly in Glasgow, Scotland December 28, 1827. 
"Scotland Census, 1851," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:VYB7-9NC : 4 November 2019), Alexander Stewart, Northern, Lanarkshire, Scotland; from "1851 England, Scotland & Wales census," database and images, findmypast (http://www.findmypast.com : 2012); citing p. 2, PRO HO 107, The National Archives UK, Kew, Surrey; FHL microfilm 1,042,417.
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It may be possible to confirm family relationships with Alexander by comparing test results with other carriers of his Y-chromosome or his mother's mitochondrial DNA.
However, there are no known yDNA or mtDNA test-takers in his direct paternal or maternal line.
It is likely that these autosomal DNA test-takers will share some percentage of DNA with Alexander: