"The Drennan-McTier letters," edited by Jean Agnew, 1998, has several references to the James Adair who I think is the "Serjeant"referred to above.
Martha McTier and William Drennan were brother and sister, children of the Rev. Thomas Drennan and Ann Lenox.Their correspondence from 1776 to 1819 takes up three very thick volumes.
Adair is referred to as "Jemmy" some of the time, and his political ups and downs are discussed, mostly with reference to how he might be helpful to the Drennan and McTier family's prospects.I didn't pick up what their relationship (if any) was to him.
The editor, Jean Agnew, is the same person who wrote "Belfast Merchants in the seventeenth century," 1996, which was mentioned somewhere here, but I can't find it now!
If this Adair is of interest to someone I could supply more.I thought the 'McTier' name close enough to 'McTyre' (as in SaraAnn Adair, daughter of James Adair of South Carolina, who married William McTyre) to be interesting, although most likely a coincidence.