Not sure if this will help you or not.
"Original Land Purchasers of Branch County, MI." book lists these Shay names :
Shay, George W. of Branch Co., MI. bought land in section 1 of Bethel Twp, entered on Jan 6, 1836.
Shay, Steven G. of Branch Co., MI, bought land in section 35 Batavia Twp, entered Oct 10, 1835.
Shay, William of Branch C o., MI. bought land in Batavia Twp. sections 28 & 32, entered Jan 29, 1833.
(wonder if this is a typo in the name ??)
McCam, Daniel, of Monroe Co., N.Y., bought land in Batavia Twp. section 35, entered Dec 23, 1835.
There are a few SHAY names in the cemetery books in Branch County, some in Batavia Twp.
In the STATE census of Coldwater Township, Branch Co., MI. are:
John Shay is a Laborer. His household consists of -
1 male under 5, 1 male over21/under45, one male married.
1 female over18/under40,1 female married.
Myron Shay is a laborer, living alone, not married.
In the STATE census of 1874 for Branch County, Michigan:
SHAY, Myron A.is a farmer in OvidTownship.
Shay, George W., 22, of Batavia Twp., m Ellen M. Hurley, 19, of Batavia Twp., on 2 Feb 1866 at Batavia Twp., bySilas N. Card (JP), witnessed by Daniel C. Card and Emly I. Card. #3165.
Shay, Franklin, 20, b Branch County, of Bethel Twp., farmer, m Harriet Dubendorf, 18, b Star Co., OH, of Bethel twp., on 17 Sep 1871, at Bethel Twp., by John Q. Adams (JP), witnessed by George F. Dubendorf and Emily Showers, both of Bethel Twp.# 4747.
Shay, Steven, of Prairie River, Branch County,m Jane N. Freeman, of the same place, on 29 March 1835, by Alfred Driggs (JP). Record # 8.
I hope this gives you an idea of who was in Branch County during certain years.
Mary in Tx.