Trying to make a connection to the MayFlower Fullers. Who was his father? My great grandmother told the family that his Fuller ancestors came over on the Mayflower. How do I go about finding this information?

Descendants of Ebenezer Fuller

1 Ebenezer Fuller b: Abt. 1784 in Reading, Windsor Co., Vt. d: Abt. 1866 in Short Tract, Allegany Co., N.Y.
. +Sarah D. White b: Abt. 1785 in Vt. d: Abt. 1866 in Short Tract, Allegany Co., N.Y. m: Abt. 1808 in Vt.
.... 2 Adeline L. Fuller b: Abt. 1809 in Reading, Windsor Co., Vt. d: Abt. 1882
........ +Joseph W. Buck b: Abt. 1807 in Reading, Windsor Co., Vt. d: 27 Mar 1892 m: 30 Mar 1831 in Reading, Windsor Co., Vt.
........... 3 George F.W. Buck b: Abt. 1834 in N.Y.
........... 3 Albertine F. Buck b: Abt. 1840 in N.Y.
.... 2 George W. Fuller b: 17 Oct 1811 in Westford, Windsor Co., Vt. d: 26 Jul 1889 in Short Tract, Allegany Co., N.Y.
........ +Mary A. Bigelow b: 25 Jan 1816 in Reading, Windsor Co., Vt. d: 11 Nov 1873 in Short Tract, Allegany Co., N.Y. m: 01 May 1836 in Reading, Windsor Co., Vt.
........... 3 Sarah L. Fuller b: Bet. 1837 - 1846 in Allegany Co., N.Y. d: Abt. 1881 in Belfast, Allegany Co., N.Y.
............... +Edward Carter b: 22 Mar 1825 in Onondoga Co., N.Y. d: 08 Jun 1906 in Southport, Chemung Co., N.Y. m: Abt. 1858
.................. 4 Cora Carter b: May 1859 in N.Y. d: Abt. 1918 in Belfast, Allegany Co., N.Y.
...................... +Thurlow B. Miner b: May 1855 in Belfast, Allegany Co., N.Y. d: Abt. 1913 in Belfast, Allegany Co., N.Y. m: Abt. 1875 in N.Y.
.................. 4 Lora M. Carter b: 07 Dec 1865 in Belfast, Allegany Co., N.Y. d: 27 Jun 1946 in Canandaigua, Ontario Co., N.Y.
...................... +John R. Dey b: May 1865 in Allegany Co., N.Y. d: 18 Feb 1903 in Caneadea, Allegany Co., N.Y. m: Abt. 1888
.................. *2nd Husband of Lora M. Carter:
...................... +Fredrick C. Fuller b: Jul 1861 d: 08 Sep 1941 in Canandaigua, Ontario Co., N.Y. m: Abt. 1910
.................. 4 Bertha Carter b: 03 Mar 1871 in Syracuse, Onondaga Co., N.Y. d: 05 Sep 1934 in Canandaigua, Ontario Co., N.Y.
........... 3 Oscar A. Fuller b: Feb 1849 in Granger, Allegany Co., N.Y. d: 23 May 1907 in Granger, Allegany Co., N.Y.
............... +Mary A. Harper/Hopper b: 13 Jan 1844 in Belfast, Allegany Co., N.Y. d: 21 Aug 1939 in Hume, Allegany Co., N.Y. m: Abt. 1869
.................. 4 Eva May Fuller b: 20 Apr 1870 in Allen, Allegany Co., N.Y. d: 23 Feb 1913 in Fillmore, Allegany Co., N.Y.
...................... +Francis J. Redmond, Dr. b: Abt. 1867 in N.Y. d: 28 Mar 1922 in Hume, Allegany Co., N.Y. m: Abt. 1900 in N. Y.
.................. 4 Flora B. Fuller b: 12 Apr 1872 in Short Tract, Allegany Co., N.Y. d: 28 Apr 1945 in Hume, Allegany Co., N.Y.
...................... +Fred John Mitchell b: 26 Feb 1876 in Mi. d: 21 Jan 1948 in Oroville, Butte Co., Ca. m: 15 Jul 1896 in Granger, Allegany Co., N.Y.
.................. *2nd Husband of Flora B. Fuller:
...................... +Milford J. Merville b: Abt. 1870 in Eagle, Wyoming Co., N.Y. d: 02 Sep 1938 in Hume, Allegany Co., N.Y. m: 15 Jul 1919 in Allegany Co., N.Y.
.................. *3rd Husband of Flora B. Fuller:
...................... +Dwight A. Arnold b: 19 Aug 1872 in Caneadea, Allegany Co., N.Y. d: 29 Feb 1952 in Fillmore, Allegany Co., N.Y. m: 26 Jun 1943
.................. 4 Mary Grace (Louise) Fuller b: Bet. 1878 - 1882 in Allegany Co., N.Y. d: Bet. 1939 - 1945 in Buffalo, Erie Co., N.Y.
...................... +(Foote) m: Bet. 1895 - 1899
........... 3 Norman Bigelow Fuller b: 15 Mar 1852 in Allen, Allegany Co., N.Y. d: 27 May 1890 in Belmont, Allegany Co., N.Y.
............... +Estelle Ernestine Marsh b: 18 Aug 1857 in West Yorkshire, Cattaraugus Co., N.Y. d: 13 Aug 1933 in Owego, Tioga Co., N.Y. m: 23 Nov 1875 in Belfast, Allegany Co., N.Y.
.................. 4 Charles Ernest Fuller b: 01 Mar 1885 in Belmont, Allegany Co., N.Y. d: 22 Mar 1931 in Scranton, Lackawanna Co., Pa.
...................... +Edna Ruth Chidester b: 29 May 1882 in Apalachin, Broome Co., N.Y. d: 14 Apr 1981 in Milford, Clermont Co., Oh. m: 15 Jun 1907 in Little Meadows, Susquehanna Co., Pa.
.... 2 Louisa M. Fuller b: 20 Jun 1815 in Reading, Windsor Co., Vt. d: 10 May 1897 in Granger, Allegany Co., N.Y.
........ +David A. Wells b: Abt. 1814 in Amsterdam, N.Y. d: 10 Dec 1895 in Granger, Allegany Co., N.Y. m: Abt. 1840 in N.Y.
........... 3 Sarah Wells b: Abt. 1841 d: Bef. 1895
............... +George Buck, Prof.
........... 3 Margaret Hall Wells b: Abt. 1862 in N.Y. d: Bef. 1895
............... +William T. Palmer
........... 3 Sarah J. Wells b: Abt. 1871 in Allegany Co., N.Y. d: 22 May 1887 in Allegany Co., N.Y.
.... 2 Alonzo W. Fuller b: 05 Mar 1818 in Burlington, Chittenden Co., Vt. d: 18 Jan 1892 in Granger, Allegany Co., N.Y.
........ +Anner Van Nostrand b: 04 Aug 1818 in Short Tract, Allegany Co., N.Y. d: 25 Feb 1904 in Granger, Allegany Co., N.Y. m: 13 Jan 1850 in Granger, Allegany Co., N.Y.
........... 3 Frederick Fuller b: 22 Apr 1851 in Granger, Short Tract, Allegany Co., N.Y. d: 11 Mar 1925
............... +Martha Ella Bennett b: Jun 1851 in Granger, Short Tract, Allegany Co., N.Y. d: 06 Mar 1929 in Hume, Allegany Co., N.Y. m: 19 Jun 1873 in N.Y.
.................. 4 Gertrude Fuller b: Jan 1874 in N.Y. d: Abt. 1956
...................... +Loomis H. Eldridge b: 22 May 1872 in N.Y. d: Dec 1967 in Warsaw, Wyoming Co., N.Y. m: 15 Dec 1897 in N.Y.
.................. 4 Mina S. Fuller b: 24 Sep 1880 in N.Y. d: 11 Dec 1950 in Fillmore, Allegany Co., N.Y.
...................... +Fred F. Bentley b: 08 Feb 1878 in N.Y. d: 23 Jul 1937 in Fillmore, Allegany Co., N.Y. m: 24 Jun 1900 in N.Y.
.................. 4 Ross L. Fuller b: Oct 1891
...................... +Elizabeth Corbett
.... 2 Ebenezer W. Fuller b: 29 Feb 1820 in Plattsburgh, Clinton Co., N.Y. d: 29 Nov 1886 in Wiscoy, Allegany Co., N.Y.
........ +Katharine H. (Fuller) b: Abt. 1821 in Vt. d: 19 Mar 1889
.... 2 Cornelia Fuller b: Abt. 1822 in Vt.
........ +William Carter b: Abt. 1815 in Onondaga Co., N.Y.
........... 3 Frances M. Carter b: Abt. 1846 in Monroe Co., N.Y.
........... 3 Mary E. Carter b: Abt. 1848 in Allegany Co., N.Y.