If we rephrase the statement "my father's son" as "me", we can simplify the riddle to "THAT man's father is me." In other words, the man being referred to is the speaker's son. This is because the speaker is saying that the man's father (who we don't know) is the same person as "me" (i.e., the speaker's father's son). The only person who fits this description is the speaker's son.

So, the answer to the riddle is "the speaker's son."

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