Hi Charles, I've been researching a David Alexander in Burke NC 1800-1810, Buncombe 1820-30 and Henderson NC.He is next door to Robert Carson in 1820 (son of my ancestor David Carson).
This David appears to be the David Whitford Alexander born 1757, son of Francis Alexander 1730 York PA - 1815 Guilford or Mecklenburg NC and Letitia Braden 1730 Guilford.
The family tree on Rootsweb lists siblings Rebecca 1769, Josiah Newton 1772, Jane 1776 and Elias Weeks 1780.Maybe your Ann is from this Alexander family.I don't yet know if it connects to my Carson line or if this is just coincidence.
Some things of possible interest:
In 1810 Burke NC, a George Penland 26-45 and Abraham Penland (page 14 on ancestry.com) are next door to a James Alexander.In 1810 Buncombe NC, a George Penland Sr 45+ is listed.Also in 1810 Buncombe NC, a George Penland 26-45 is about 20 households from my David Carson ancestor (4g gf).This George is also 4 households from Samuel Queen (my 4g gf whose dtr Nancy later married Samuel Carson, my 3g gf).My analysis indicates that Robert Carson in 1820 Bunbombe was near where David had been in 1810, based on some similar neighbors.
A particular finding of interest to me was that George Alexander's sister Jane married David McCord.My Carson line in Lancaster PA earlier connects to the McCord line there and later in TN.
Maybe there are some connections for you here with this Alexander family.