The generalized quote about the sins of the father being laid upon their sons is most closely and nearly related to a quote in Shakespeare’s Merchant of Venice.
“The sins of the father are to be laid upon the children.”

However very similar sentiments appear in the Christian Bible from which the Merchant of Venice line is likely derived….

In Deuteronomy Chapter 5
” You shall not bow yourself down to them, nor serve them. For I the LORD your God am a jealous God, visiting the iniquity of the fathers upon the sons to the third and fourth generation of those who hate Me, and doing mercy to thousands of those who love Me and keep My commandments.”

In Jeremiah Chapter 32
“Ah, Lord Jehovah! You have made the heavens and the earth by Your great power and stretched out arm. Nothing is too great for You. You show loving-kindness to thousands, and repay the iniquity of the fathers into the bosom of their sons after them.”

Even earlier Greek dramatist Euripides wrote in Phrixus, …
“The gods visit the sins of the fathers upon the children.”

Roman Poet Horace wrote…
…”For the sins of your fathers you, though guiltless, must suffer. The sins of the father are to be laid upon the children.”

The concept seems cruel and unfair to us today. I am not philosophically nor theologically inclined and claim no training therein. However, I don’t see the concept as an unfair threat or bullying but a simple warning of a fact of life. Maybe the old Testament phrasing suggests that God’s jealousy exacts the punishment upon lineages but then maybe the phrasing is simply a warning that the nature of God’s world is that your actions will affect your children and your lineage. We can see logically and dispassionately that such is true. Behaviors by parents and even neighbors can have lingering good or dire effects on those that follow for generations. Adherence to a moral code, specifically in the old Testament, that passed down in the Hebrew lineage, will make life easier and kinder to a degree for you and your lineage.

Describing the concept of the sins of the parents being visited upon their offspring as unfair is much like describing gravity as unfair if you step off a cliff. It is just a consequence.

Parents are of course not perfect. Ideally they would always teach beneficial behaviours by example but that won’t always be possible as they struggle under exposures and behaviors from their ancestry. The best that can be hoped for then is to expose their kids to other folks who do certain aspects of life better and to pass along the very real truth that the sins of the father are visited upon the children so that they too can try to give their children exposure to virtue.