Hello,I have a question here.
What's the difference between "He is a friend of my father's" and "He is a friend of my father"?
I am not sure whether there is something wrong with the second sentence or not.
Thanks in advance for your help.

Question

Answer

There is no difference in meaning.

Both are correct, in spite of the fact that the apostrophe + 's' seems unnecessary/ superfluous.

Both are commonly used: at least when talking about people. 
(So for example you would not say *"the legs of the table's"*, but: "the legs of the table".)

Why can you say both? Well there is a lot of debate about that among grammarians - but no really conclusive answer.

You can often find this type of 'double genitive', or 'double possessive' in English, going back to Shakespeare...
🙂

Answer

Charlie is correct. Both are acceptable and convey the same meaning: this man is friends with your father.

Answer

first is not correct, second is. "father's" is possessive. You could say "He is a friend of my father's boss". Or, "He is my father's friend".