"When my son was born, he had six fingers on his right hand."
Translation:Kiam mia filo naskiĝis, li havis ses fingrojn sur la dekstra mano.
When you use "lia" it becomes a bit ambiguous, because it can be referring to any masculine third-person. "Sia" makes it clear that it's his own hand.
I would go further than just "can be referring" and insist that in a sentence "Kiam mia filo naskiĝis, li havis ses fingrojn en (sur) lia dekstra mano." those two cases of the pronoun "li" must be referring to different persons. In that case the sentence becomes even more weird.