Deuteronomy 24:16
The fathers shall not be put to death for the children, neither shall the children be put to death for the fathers: every man shall be put to death for his own sin. The fathers shall not be put to death for the children, neither shall the children be put to death for the fathers: every man shall be put to death for his own sin.
The verse belongs to the law that Moses commanded and wrote as the human author of the Pentateuch, an authorship affirmed by Jesus. It stands among the repeated laws in Deuteronomy 23-25 concerning duties between person and person and between person and God. It commands personal administration of capital punishment, so that fathers are not to be put to death for children's sins nor children for fathers' sins, but every person is to be put to death for his own sin. Each person is accountable to God individually for his own sin, and dies for that sin.
Amaziah applied the verse when he executed the servants who had killed his father but spared their children, establishing that punishment for a crime is personal. God holds each person individually accountable and never condemns any infant or adult for another person's wrong at any time, even for a wrong done thousands of years before birth. Guilt and righteousness rest only on the doer, a truth given to Israel early in their history. The penalty taught by the verse is death for one's own sin, so each bears the consequence of his own sin and not another's, and the wicked are not given eternal life.
The verse denies that guilt is passed from Adam to his distant offspring. What fallen parents pass on is a bent toward evil that is strengthened by each person's own evil acts, so death comes to all because all themselves do wrong. The command about the effects of parents' iniquities on children does not require a child to die for a parent's wrongdoing. Those effects are inherited diseases and other physical harms that correct living and temperate habits, with God's blessing, can measurably lessen.
Neither a man's family nor the community at large is held responsible for his wrongdoing, and neither can bear his guilt or supply salvation from its results. The one who sins needs personal salvation and cannot lay blame on society or look to the salvation of society. A child's unknown or illegitimate parentage is not that child's fault, does not make the child responsible for another person's sin, and does not exclude the child from salvation. Children do not bear a parent's guilt, and parents do not bear a child's guilt.