Let's analyze the statement step-by-step:

Statement:

A woman said:
"His mother is the only daughter of my father."

Breaking it down:

• "My father" refers to the woman's father.
• "The only daughter of my father" means the woman herself (since she is the only daughter of her father).
• "His mother is the only daughter of my father" means his mother is the woman herself.

Conclusion:

• The man’s mother is the woman who is speaking.
• Therefore, the man is the woman's son.

Final answer:

The man is the woman's son.