Finding my Wife’s half Sister

My wife’s mother and father are both dead and she has no siblings that she knows. Her biological father died when she was about 3-4 years old and her dad and mom were not married. I have his full name and yet I cannot find anything on him except maybe some old addresses. Apparently he had a daughter before having my wife and so I would really like to find her as she has no family hardly and has lost hope in ever finding her. I tried, but it’s not an easy task for myself.