Hello Bev
Found a William Martin on the 1920 census born around 1907. He lived in Alexandria, VA. Here are the members of the household:
Bernard B Martin 49
Emma L Martin 33
Mary O Martin 20
Claudie Martin 18
Theophilus Martin 17
Ardie L Martin 15
William Martin 13
Osary L Martin 12
Joseph Napper 27
Not sure if this is your William or not. Do you know the names of your grandparents and do you know your mother's maiden name?
Provide some more info and I will see what else I can dig up.
Peace and Blessings.
April