His death certificate has 1883 as his birth year and 1950 for his death year. His headstone has 1882 and 1951. 1900 census has 1883.

Kentucky, Death Records, 1852-1963
Name: James A. Simmons
Death Date: 2 Jan 1950
Death Location: Barren, Kentucky, USA
Age: 66
Gender: Male
Race: White
Birth Date: 15 Dec 1883
Birth Location: Kentucky
Father's name: H B Simmons
Mother's name: Elizabeth Shirley

1900 United States Federal Census
Name: James A Simons
Age: 17
Birth Date: Dec 1883
Birthplace: Kentucky
Home in 1900: Horse Cave, Hart, Kentucky
Race: White
Gender: Male
Relation to Head of House: Son
Marital Status: Single
Father's name: Henry B Simons
Father's Birthplace: Kentucky
Mother's name: Katie Simons [should be step-mother.]
Mother's Birthplace: Kentucky
Household Members: Name Age
Henry B Simons 44
Katie Simons 19
James A Simons 17
Mary E Simons 7
Lizzie L Simons 2
Joe Ann Simons 6/12

1910 United States Federal Census
Name: Jim Simmons
Age in 1910: 27
Birth Year: abt 1883
Birthplace: Kentucky
Home in 1910: Slick Rock, Barren, Kentucky
Race: White
Gender: Male
Relation to Head of House: Head
Marital Status: Married
Spouse's Name: Martha Simmons
Father's Birthplace: Kentucky
Mother's Birthplace: Kentucky
Household Members: Name Age
Jim Simmons 27
Martha Simmons 20
Susie Simmons 4
Lucy Simmons 4/12

1920 United States Federal Census
Name: J A Simmons
Age: 37
Birth Year: abt 1883
Birthplace: Kentucky
Home in 1920: Edmonton, Metcalfe, Kentucky
House Number: Farm
Race: White
Gender: Male
Relation to Head of House: Head
Marital Status: Married
Spouse's Name: Martha Simmons
Father's Birthplace: Kentucky
Mother's Birthplace: Kentucky
Able to Speak English: Yes
Occupation: Harme
Industry: General
Employment Field: Employer
Household Members: Name Age
J A Simmons 37
Martha Simmons 35
Susie Simmons 14
Lucy Simmons 10
Mary Simmons 8
Brach Simmons 6
Annie Simmons 3 2/12

1930 United States Federal Census
Name: James A Simmons
Birth Year: abt 1883
Gender: Male
Race: White
Birthplace: Kentucky
Marital Status: Married
Relation to Head of House: Head
Home in 1930: District 3, Barren, Kentucky
Street address: Edmonton Road
Dwelling Number: 144
Family Number: 148
Home Owned or Rented: Rented
Radio Set: No
Lives on Farm: Yes
Age at First Marriage: 22
Attended School: No
Able to Read and Write: Yes
Father's Birthplace: Kentucky
Mother's Birthplace: Kentucky
Able to Speak English: Yes
Occupation: Farmer.
Industry: General Farm
Class of Worker: Working on own account
Employment: Yes
Household Members: Name Age
James A Simmons 47
Ina Simmons 29
Henry B Simmons 16
Annie P Simmons 13