how to find a father i never met in my lifetime

Well, he had never been a part of your life, your mother never mentions him or talks about him, so the question is why would you want to bother looking him up? Something tells me that if he wanted a relationship with you, he would probably have had one. I would let it go.

I last saw my father at about the age of three or four. I heard only his bad side. But, at about age 38, I decided I had to find out about him. The only place I knew to start was a dead end search. So I dropped it and waited more years. After I got my first computer, I typed his full name into the search bar and the first hit was a genealogy chart with his name, as well as dozens of relatives I had never known. It was on Ancestry.com. These days it might not have happened like that, as the charts are more closely guarded. But they had and maybe still have a message board. I made repeated pleas for contacts, until I got the notice of a first cousin living in Dallas. Through this man I got to see a better rounded picture of my father, who had died in 1948. My mother no longer loved him, but these people did and still do. But, also, If you know his full name and birth date, you might find his information through the Social Security.

grab your birth certificate and look him up in whitepages

Hire a good private detective.
Thay used to do good, successful work, for me.
Thay were quick and cost little.