Could the iniquity of the fathers visit the children as the Bible says in (Ex. 20:5) and as we say “The fathers ate sour grapes and the children’s teeth are set on edge”?
The fathers can hand down to their children physically the result of their sins or sicknesses.
The parent could sin and as a result of his or her sin they may have contract a sickness and then the son or the daughter could inherit that sickness. The children could be stricken by mental or neurological diseases, some blood disorders or congenital defects as a result of what was inherited from their parents.
Often the sickness of the children and their suffering are a cause of pain for the parents especially if they knew that the sickness was a result of their sins.
The children might inherit ill-nature or bad character from their parents.
But this is not a rule; king Saul was cruel, merciless and of bad character. His son Jonathan was the opposite. Jonathan was a friend of David. He loved him and was faithful to him.
Even if the children inherit ill-nature from their parents, they can with ease get rid of it if they wish.
A son can inherit poverty or debts because of his father’s mistakes…
He suffers because of it, of course on earth, and that would have nothing to do with his eternal life. Many are the end results that the saying of the poet agrees with (This is what my father inflicted upon me, and I did not inflict on anyone). As for judging the children for the sins that were committed personally by their parents, the Bible has refuted completely as written in he Book of Ezekiel “what do you mean when you use this proverb… the fathers have eaten sour grapes, and the children’s teeth are set on edge? ‘As I live’ says the Lord God, you shall no longer use this proverb the soul who sins shall die… “
The son shall not bear the guilt of the father, nor the father bear the guilt of the son:
“The righteousness of the righteous shall be upon himself, and the wickedness of the wicked shall be upon himself. (Ezek. 18:1-20).
The righteous Jonathan did not bear the evil of his father king Saul nor Josiah the righteous king the sin of Aaron his father or Manasseh his grandfather or the rest of his forefathers.
The curses of the law in the Old Testament was abolished in the New Testament. As we say in the Anaphora of St. Gregory:
[You have lifted the curse of the Law].
As an example of this curse, Canaan, did bear the curse of his father Ham, (Gen. 9:22-25) and his sons also bore it till the days of the Lord Christ and not only till the fourth generation.
Now, we are in the era of “grace and truth” (John 1:17) so do not be afraid of the curse of the Law which was inherited by the children from their grandfathers.
Often the father could be evil but the son is righteous refusing to walk in his father’s footsteps, and even he might resist him as the Lord says, “He who loves father or mother more than Me is not worthy of Me.” (Matt. 10:37).
Naturally it would be unjust for God to visit the sins of this evil father on his righteous son who deserves to be rewarded.