how to find my dad

Talk to your mother.

My mother is deceased and none of my relatives know him. I have some useful (I think) information about him for example: he grew up in Michigan, US and he has a married brother. Can that help?

You're still dealing with a very large number of people in the pool of candidates.

With your mother gone, you still might be able to get some ideas from your relatives. If you have aunts and uncles, they might have some ideas. There are your mother's living friends, and the people she went to school with. If, say, she knew your father while she was in high school, that might provide some clues.

At some point, though, you might want to consider hiring a private detective or a skip tracer.