Let’s look at some examples of the rule, from most to least obvious: The man is a friend of mine (not “of me”). The man is a friend of David’s (not “of David”). The man is a friend of your mother’s (not “of your mother”). The man is a friend of Tom's father's (not “of Tom’s father”). Strangely enough, the formal rules of English grammar do indeed require the use of the possessive ending in this phrase. There is a reasonable sounding explanation, but in reality, I would ignore this rule in your example, since it would just sound unnatural.

Hi Patricia, The correct sentence is: "This man is a friend of Tom's father." The possessive indicator ('s) is not needed after "father" because the word "of" after "friend" already tells us what we need to know. I hope I've helped answer your question. Please let me know if I haven't.