Faulkner, James ? of Steuben County, N.Y. Member of New York state assembly from Steuben County, 1803-04. Burial location unknown.

Dansville History:
The 1810's--Locals fight in War of 1812. Rufus Stone founds Stone's Falls. A young Millard Fillmore lives in Dansville area for six months. First local Masonic lodge organized. James FAULKNER takes up medicine in Dansville.
The 1820's--Livingston County created; Dansville annexed into town of Sparta.

The Dansville Advertiser
Dansville, Livingston Co., New York
January 31, 1884
Dr. James FAULKNER of this village was 94 years old last Monday.

This posting on rootsweb lists the heirs of James Faulkner:

James Faulkner, born Cambridge, [Washington Co] NY, 21 Jan. 1790, was the son of Samuel Faulkner (according to an online tree Samuel was b. 26 SEP 1765 in Bedminster, Somerset Co, NJ.) and Catherine PHENIX (according to an online tree she was b. 31 DEC 1768). He married, at Dansville, NY, 12 May 1812, Minerva Hammond, and was a prominent citizen of North Dansville, Livingston Co, NY. I do not know the names of his brothers and sisters, but I have a record of his descendants for several generations, from genealogies, wills, and land records.
Samuel FAULKNER died in Geneseo, then part of Ontario County in 1805. A wife, Catherine and children were living but the children were not named in the probate material. Seeking information on descendants of this family.
Abstract of the Will of James Faulkner, of Dansville, dated 3 Sept. 1878, proved 28 Feb. 1885

Names

Grandson James F. Bryant (child of deceased daughter Catherine Bryant), and
Grandson William C. Bryant (child of deceased daughter Catherine Bryant), land lately occupied by said daughter in Ossian, 160 acres,

Mary Simons, sister of James and William Bryant
Elizabeth Woods, sister of James and William Bryant
Catherine Aldrich, sister of James and William Bryant

Son-in-law William C. Bryant

DeWitt Bryant, brother of William C. Bryant, Sr.

Leonard Kuhn

Son James Faulkner Jr - much land in Livingston and Allegany Counties

Son Lester B. Faulkner - much land in Ossian and Dansville

Grandson Henry J. Faulkner - land in Canadice, Ontario County, NY (Lot #4, 5th Range, 113 and more acres)

Daniel C. Howell

Fanny B. Williams, deceased

John C. Williams, husband of Fanny B. Williams

Grandchildren (children of Fanny B. Williams) all under 21

Granchildren (children of James Faulkner, Jr)

Grandchildren (sons of John C. and Fanny B. Williams): James J. Williams, Edward H. Williams - land in Hancock, Waushura County, Wisconsin (s 1/2 SE Quarter, Section 10, Township 19, Range 8, 80 acres, plus N 1/2 E Quarter, Section 15, Township 19, Range 8, 80 acres)

Grandson Samuel Faulkner, son of James Faulkner, Jr.

Grandson James Faulkner, son of James Faulkner, Jr.

Granddaughter Maggie Faulkner - a farm in North Dansville

Granddaughter Minerva F. Williams

Granddaughter Minerva Faulkner* (daughter of James Faulkner)

Nancy Brewer - house she lives in for life

Jacob J. Folly

Henry J. Faulkner

Executor: James Faulkner Jr., Lester B. Faulkner, Henry J. Faulkner

CODICIL, dated 11 Jan. 1881
Pertaining to acquisitions from the estate of son Samuel D. Faulkner, deceased, a member of the firm of Sweet, Faulkner, & Co., at the time of his death

CODICIL, dated 29 April 1884,
Adds nothing to the list of heirs.

* MISS MINERVA FAULKNER
Rochester, Monroe, NY
Democrat & Chronicle
Sun Jan 3, 1937
Dansville - Funeral services for Miss Minerva Hammond FAULKNER, 76, who died Friday in the home of her nephew, Ward HUNTER in Bronxville, will be in the home of her brother, Samuel D. FAULKNER 52 Elizabeth Street, Tuesday at 2 p.m.

Here's another piece of the puzzle from USGENWEB Livingston Co NY:
CONCERNING NORTH DANSVILLE:
Among the other settlers were Daniel P., Samuel, and James FAULKNER, Nathaniel and William Porter, from Penn., in 1796; Jacob Welsh, Jacob Martz, and his son Conrad, George Shirey, and Frederick Barnhart, Penn., 1798. William PHENIX, James Logan, David Sholl, and John Vandeventer, were also early settlers. The first marriage was that of William McCartney and Mary McCurdy. Thomas McLain taught the first school, in 1798 of '99; Samuel Faulkner kept the first inn, in 1796; Daniel P. Faulkner, the first store, in 1797 and 1798; David Scholl erected the first sawmill, in 1795, and the first gristmill, in 1796. Mr Scholl was Charles Williamson's millwright, and built the mills for the Pulteney Estate...

From the "Ninth Annual Meeting of the Livingston Historical Society": an autobiography
[abbreviated below]

He left Cambridge with his father Dec 26, 1796
Arrived in Dansville, NY abt Jan 7, 1797 [William and John Phenix were first recorded there in 1799]
In June 1801he and his father moved to Geneseo [now Livingston Co] and died there in 1805
In 1807 he moved to Painted Post and began to study medicine
Stayed in Steuben Co until 1810, wintered in NYC studying medical lectures
In 1811 he waas licensed to practice medicine in Bath
In 1812 he married and moved back to Dansville the month after his marriage
For the next 2 years he was Justice of the Peace, the next year town Clerk of Dansville
The next year he was made Postmaster and held the office 26 years
From Oct to Dec 1813 he was in the War of 1812
"stayed long enough to get a pension and 160 acres of land"

• Married: 12 May 1812 in Dansville,Steuben,NY

1. Catherine F FAULKNER b: 29 Apr 1816 in Dansville,Steuben,NY
2. Endress FAULKNER b: 25 Mar 1818 in Dansville,Livingston,NY
3. Fanny Bradner FAULKNER b: 7 Aug 1825 in Dansville,Steuben,NY
4. Amariah H FAULKNER b: 7 Aug 1825 in Dansville,Livingston,NY
5. Samuel D FAULKNER b: 22 Aug 1827 in Dansville,Livingston,NY
6. Mary B FAULKNER b: 15 Sep 1830 in Dansville,Livingston,NY
7. James FAULKNER Jr b: 22 Jan 1833 in Dansville,Livingston,NY
8. Samuel Dorr FAULKNER b: 14 Nov 1835 in Dansville,Livingston,NY
9. Lester B FAULKNER b: 4 Apr 1837 in Dansville,Livingston,NY