The man being referred to in the riddle is the speaker's son.
The riddle states that "THAT man's father is my father's son." To determine who "my father's son" is, we need to consider who the speaker is. The riddle doesn't give us any information about the speaker's gender, so we can't assume that the speaker is male or female. However, we can assume that the speaker is referring to themselves, since they use the first person singular pronoun "I".