In reply to your query: John Cole b. 1782 Carmel, NY, was the son of Elisha Cole 26 Jan 1743 Eastham, Mass.-- 3 Feb 1826 Carmel, NY & Charity Hazen 1744-1811 Carmel, NY.
His father was Elisha 1717--1801 Carmel, NY and his mother was Hannah Smalley 1720 Eastham, Mass.--1811 Fredericksburg, NY.
This family is from my maternal side. The documented beginning of the clan was James Cole 1584-1630.
If you need more info don't hesitate to ask!!