Does it say anywhere in the Bible that the sins of the fathers are visited on their children?

I heard this saying, however, I haven't yet been able to find anything in the Bible to back up such a saying.

If anybody can shed some light on this, it would be most appreciated.

Exodus 20:5
you shall not bow down to them nor serve them. For I, the LORD your God, am a jealous God, visiting the iniquity of the fathers upon the children to the third and fourth generations of those who hate Me,

Exodus 34:7
keeping mercy for thousands, forgiving iniquity and transgression and sin, by no means clearing the guilty, visiting the iniquity of the fathers upon the children and the children’s children to the third and the fourth generation.”

Numbers 14:18
‘The LORD is longsuffering and abundant in mercy, forgiving iniquity and transgression; but He by no means clears the guilty, visiting the iniquity of the fathers on the children to the third and fourth generation.’

"Visiting the iniquity of the fathers upon the children unto the third and fourth generation of them that hate Me." It is inevitable that children should suffer from the consequences of parental wrongdoing, but they are not punished for the parents' guilt, except as they participate in their sins. It is usually the case, however, that children walk in the steps of their parents. By inheritance and example the sons become partakers of the father's sin. Wrong tendencies, perverted appetites, and debased morals, as well as physical disease and degeneracy, are transmitted as a legacy from father to son, to the third and fourth generation. This fearful truth should have a solemn power to restrain men from following a course of sin. {PP 306.3}

God will not lightly esteem the transgression of His law. "The wages of sin is death." The consequences of disobedience prove that the nature of sin is at enmity with the well-being of God's government and the good of His creatures. God is a jealous God, visiting the sins of the fathers upon the children to the third and fourth generations of them that hate Him. The results of transgression follow those who persist in wrongdoing; but He shows mercy unto thousands of them that love Him and keep His commandments. Those who repent and turn to His service find the favor of the Lord; and He forgiveth all their iniquities and healeth all their diseases. {RC 52.4}

Very well done!

Here's the follow-up: Did Adam's choice to sin result in Cain's needing an atoning sacrifice from birth? Or did Cain need one only after he chose to sin himself?

Adam's choice resulted in his needing to be reconciled to God, which is what "atonement" or "at-one-ment" is about. Without the reconciling sacrifice of Christ, Adam would have been lost. He was only able to exist because of Christ.



Now if Adam had ceased to exist, then Cain would not have existed, so Cain was always dependent upon the sacrifice of Christ, not just after he sinned.

"All have sinned", therefore, all need a Saviour. We need a Saviour because we ourselves have sinned - not because Adam ate the forbidden fruit. We are not guilty of Adam's sin.

Ezekiel
18:20 The soul that sinneth, it shall die. The son shall not bear the iniquity of the father, neither shall the father bear the iniquity of the son: the righteousness of the righteous shall be upon him, and the wickedness of the wicked shall be upon him.

I see what you're saying. But it's not exactly what I was talking about.

Apart from Cain's need for Adam to survive long enough to procreate, did he directly need an atonement for himself because of Adam's choice? IOW, at birth, before consciously choosing to do anything contrary to God's will, did Cain need to be reconciled to God?

Guilt is a tricky word that I want to stay away from at this time. So I'm going to avoid it.

Let me try to get a better grasp of what you're saying. At birth, did Cain need a Savior from the 2nd death?

...
Eze 18:19 Yet say ye, Why? doth not the son bear the iniquity of the father? When the son hath done that which is lawful and right, [and] hath kept all my statutes, and hath done them, he shall surely live.
Eze 18:20 The soul that sinneth, it shall die. The son shall not bear the iniquity of the father, neither shall the father bear the iniquity of the son: the righteousness of the righteous shall be upon him, and the wickedness of the wicked shall be upon him.
Eze 18:21 But if the wicked will turn from all his sins that he hath committed, and keep all my statutes, and do that which is lawful and right, he shall surely live, he shall not die.
Eze 18:22 All his transgressions that he hath committed, they shall not be mentioned unto him: in his righteousness that he hath done he shall live.
Eze 18:23 Have I any pleasure at all that the wicked should die? saith the Lord GOD: [and] not that he should return from his ways, and live?
Eze 18:24 ¶ But when the righteous turneth away from his righteousness, and committeth iniquity, [and] doeth according to all the abominations that the wicked [man] doeth, shall he live? All his righteousness that he hath done shall not be mentioned: in his trespass that he hath trespassed, and in his sin that he hath sinned, in them shall he die.
Eze 18:25 Yet ye say, The way of the Lord is not equal. Hear now, O house of Israel; Is not my way equal? are not your ways unequal?
Eze 18:26 When a righteous [man] turneth away from his righteousness, and committeth iniquity, and dieth in them; for his iniquity that he hath done shall he die.
Eze 18:27 Again, when the wicked [man] turneth away from his wickedness that he hath committed, and doeth that which is lawful and right, he shall save his soul alive.
Eze 18:28 Because he considereth, and turneth away from all his transgressions that he hath committed, he shall surely live, he shall not die.
Eze 18:29 Yet saith the house of Israel, The way of the Lord is not equal. O house of Israel, are not my ways equal? are not your ways unequal?
Eze 18:30 Therefore I will judge you, O house of Israel, every one according to his ways, saith the Lord GOD. Repent, and turn [yourselves] from all your transgressions; so iniquity shall not be your ruin.
Eze 18:31 Cast away from you all your transgressions, whereby ye have transgressed; and make you a new heart and a new spirit: for why will ye die, O house of Israel?
Eze 18:32 For I have no pleasure in the death of him that dieth, saith the Lord GOD: wherefore turn [yourselves], and live ye.

Humans sure are stubborn. God must have much patience.