A little more information would be helpful, such as your father's approximate year of birth and where and if he is still living or not.
Name: Theodore J. Herndon
Last Residence: 11412Jamaica, Queens, New York, United States of America
Born: 17 Apr 1926
Died: 10 Nov 1988
State (Year) SSN issued: New York (Before 1951 )
I found a Theodore Herndon married to an Elizabeth who has a son named Theodore (age 4) and a daughter named Delores living in New York City in 1930.Could this be them? They are African-American. I can give you the whole listing if it's a match, and perhaps more information.