The U.S. Indian Census records show a Betsey King's approximate year of birth as varying from about 1814 to 1818. It is possible there is more than one Betsey King, so you may have to sort out which is yours. Here they are in census order; and includes all Kings on same pages. I realize that a relationship is only shown between Betsey and Cornelius; but there is an outside chance that one of the other Kings is related to the original spouse of Betsey.
July 1886, Allegany reservation:
No. 518, Winston King, age 44
No. 519, Mary King, age 44
No. 520, Jennie King, age 25
No. 521, Betsey King, age 69
No. 522, Mary P. King, age 48
(No relationships listed; some others on page do show)
10 Aug 1888 Cataragus Res:
(No roll numbers listed)
Winston King, 46
Jennie King, 27
Mary King, 46
Betsey King, 71
Mary P. King, 51
June 1889 on the Cattaragus reservation:
Roll number 518, Winston King, age 47
Roll number 519, Jennie King, age 28
Roll number 520, Mary King, age 47
Roll number 521, Betsey King, age 72
30 Jun 1892, Allegany Res.
Betsey King is listed as 74, roll number 535. Other Kings listed on the page include: Norton age 49, roll number 532; Jennie, age 30, roll number 533; Mary, age 49, roll number 534 (likely the wife of George.)
30 Jun 1892 (family listed again, on Seneca roll, this time with Cornelius Fatty)
No. 528, Winston King, 50
No. 529, Jennie King, 31
No. 530, Mary King, 50
No. 531, Betsey King, 75
No. 532, Cornelius Fatty, 9, grandson
(Could be Betsey's or Winston's grandson)
30 Jun 1893, Allegheny Seneca
547, Winston King, 51
548, Jennie King, 32,
549, Mary King, 51
550, Betsey King, 76
551, Cornelus Fatty, 10, grandson
552, John King, 58
553, Emma King, 47
June 1898, Allegany Res.
584, Betsey King, 81
585, Cornelius Fatty, 15, grandson
586, Jennie King, 37
587, Lucina King, 40
588, Mary King, 56
June 1898: Betsey King, age 84, roll number 505, in the household of Willett B. Jimerson, age 54, roll number 503; Amelia Jimerson (wife)age 36, roll unmber 504. Willett H. Jimerson (son), age 23, roll number 505; Carrie Jimerson, (wife of the son) age 20, roll number 506.
June 1899, Allegeny res.
621, Betsey King, 82
622. Cornelius Fatty, 16, grandson
623, Jennie King, 38
624, Lucina King, 41
625, Mary King, 57
June 1900, Allegeny res.
621, Betsey King, 83
622, Cornelius Fatty, 17, grandson
623, Jennie King, 39
624, Lucina King, 42
625, Mary King, 58
On 30 June 1904, Allegeny Res.
She is in the household of George Gordon:
George Gordon 61 Head
Ernest Gordon 14 son
Olive Gordon 10 daughter
Betsey King 87 (ditto mark) (can't be his daughter)
1905, Allegany Res.
236, George Gordon 62
237. Ernest Gordon 15
238, Oliver Gordon 11
239, Betsey King 88 Mother-in-law
Since the earliest Betsey King I could find was born circa 1814, I did a search using a five-year birth-year parameter, and only the name Betsey, keyword Seneca. I found a Betsey Eels, married to James Eels. They are enumerated on some of the same dates as your Betsey King, so I ruled this out as a connection. I ruled out Betsey Sundown and Betsey White for the same reasons.
I do believe the Betsey King in the Gordon family is your Betsey, so she would have been alive in 1905. It is also more likely, based on those census records, that her birth year was closer to 1817-1818.
Regarding Cornelius: In July 1885, he was listed as age 2, living with his father, George A. Fatty, age 39. His mother may have died, or the parents separated. There is further data on him after 1905 in the Indian census records.
Cornelius is also on the 1900 U.S. Federal Census, living in Red Horse, Cattaraugus, New York. His date of birth is listed as February 1880. Cornelius is in household 73-73, a boarder with Lucina John.
On the same page with Cornelius is Betsey King, head of household 70-70. Her birth date is listed as April 1817. She notes she has given birth 5 times and only one child is living. She has a daughter living with her (the only living child), named Ivy or Axy. It is difficult to decipher the last name. It appears to be Gordon. She is 37 years old, born May 1863.Ivy or Axy has given birth 7 times and 5 children are living. Betsey, Ivy and Cornelius are all listed as Seneca Indian.You should look at this census to see if you find a different interpretation of spelling for the daughter. I can't confirm her on any of the Indian census records.
A relative of your Cornelius Fatty may be FATTY, Cornelius died 3-1878 age 34 - Co. E 88 th PENN. Rect NYS Vols. He is buried in Memorial Heights Cemetery, also known as Breed Run Cemetery, in Salamanca, New York. That cemetery was relocated due to the construction of the Kinzua Dam. Many Seneca and Cornplanter Indians were relocated because of the dam.
For possible parents of Betsey King, I would check out: David King, James King, William King, and Young King. All were Seneca who had lived on the Cattaragus Reservation and died in the War of 1812. Of course, King could be Betsey's mother's maiden name; but if so, may still be related to one of these men.
I also recommend you check out the follwoing microfilm rolls through NARA, or your local Family History Library, for possible information on the family lines:
• 1877-1878 Census roll. 7RA78, roll 1.
• 1885-1939 Census rolls. M595, rolls 411-416, 488-489.
• Circa 1887 Allotments. 7RA26 1, rolls 1-2.
• 1890-1893 Tribal election minute book. 7RA150, roll 3.
• Circa 1900 Register of Indian families. 7RA150, roll 1. 1910-1911 Quapaw Agency
• Competency Commission reports. 7RA36, roll 1.
• 1911-1936 Record of heirship. 7RA150, roll 2.
• 1931-1934 Supplemental census rolls. 7RA150, roll 1.
I hope all this is not repeat information and that you find it some help in your search.