@how2finddadjohndoe,
A degree would have to be exceptionally specific for it to be at all useful in your search. The only place I can even think of searching is LinkedIn, unless you know a that person's alma mater. A search for
BA Physics brings up 157 million search results. There's over 65,000 such results on LinkedIn, but at least they're more closely associated with people, rather than programs where you can get a Bachelor's degree in Physics.
If you want to intelligently look for your father, then you need to get more information from your mother. Name, approximate age, where she knew him from, names of any of his family members or friends, etc.
Be your own detective. Do some legwork. This means getting offline and talking to people.