The Bible is very clear that we are not held accountable, responsible or guilty for the sins of our ancestors.
Fathers must not be put to death for what their children do, nor children for what their fathers do; each must be put to death for his own sin (Deuteronomy 24:16 NET)
When that time comes, people will no longer say, 'The parents have eaten sour grapes, but the children's teeth have grown numb.' Rather, each person will die for his own sins. The teeth of the person who eats the sour grapes will themselves grow numb (Jeremiah 31:29,30 NET)
The word of the LORD came to me: "What do you mean by quoting this proverb concerning the land of Israel, "'The fathers eat sour grapes And the children's teeth become numb?' "As surely as I live, declares the sovereign LORD, you will not quote this proverb in Israel anymore! Indeed! All lives are mine– the life of the father as well as the life of the son is mine. The one who sins will die. (Ezekiel 18:1-4 NET)
Nevertheless, the Bible is equally clear that we can and do suffer for the sins of our ancestors.
You shall not bow down to them or serve them, for I, the LORD, your God, am a jealous God, responding to the transgression of fathers by dealing with children to the third and fourth generations of those who reject me, and showing covenant faithfulness to a thousand generations of those who love me and keep my commandments. (Exodus 20:5,6 NET)
You show unfailing love to thousands. But you also punish children for the sins of their parents. You are the great and powerful God who is known as the LORD who rules over all. (Jeremiah 32:18 NET)
"God designed families to be modeled on His parenthood, but, as many of us know, that’s often the exception rather than the rule. God intended our parents to be the most meaningful people in our lives as we’re growing up, but they’ve been influenced by the limitations of their upbringing. Whether we think about it or not, we all belong to a family line and are affected by it for good or for ill. To some degree, generational sin and generational blessing affect us all, whether or not we recognize it. We’re influenced in countless ways by the family we’ve been born into – physically, psychologically, emotionally, behaviorally, spiritually – this influence affects almost every aspect of life." (2)
"I believe that this visiting of iniquity means that we receive into our lives the consequences of our ancestor’s sins. Sometimes this visiting of iniquity, or propensity to sin, means that we end up committing the same sins as our ancestors. As we see our own brokenness, in the light of our ancestors, we can come before God and identify with their sin and our own. We may not have done the exact things they have done, but to be free we need to forgive our ancestors for their sins which have affected us in any way, and, if appropriate, we need to humble ourselves and confess to God that their rebellion and arrogance is also trapped in our hearts." (2)
"Sometimes we want to blame every present problem on generational sin, which sends us repeatedly digging into our past. We’re unwilling to bring our own sin into the light because we feel ashamed. However, because God is holy, He asks us to come to Him in reality and uncompromising honesty, relying on His grace. Like Nehemiah, we can pray a prayer of identification." (2)
Those truly of Israelite descent separated from all the foreigners, standing and confessing their sins and the iniquities of their ancestors. (Nehemiah 9:2 NET)
However, when they confess their iniquity and their ancestors' iniquity which they committed by trespassing against me, by which they also walked in hostility against me (Leviticus. 26:40 NET)
"No-one need stay trapped in generational sin, under a generational curse, because Jesus has done all that’s necessary to break its power. He’s ransomed us (purchased our freedom) from the futile (empty and worthless) ways we’ve inherited from our forefathers, by paying the redemption price. Through Him, the hereditary chain of sin is broken by something infinitely more precious than silver or gold, which will eventually perish. Only His death on the cross has the infinite power to liberate us and put within us burning hearts, abandoned to Him, and overflowing with divine love." (2)
You know that from your empty way of life inherited from your ancestors you were ransomed– not by perishable things like silver or gold, but by precious blood like that of an unblemished and spotless lamb, namely Christ. (1 Peter 1:18,19 NET)
As children, we do suffer for our parents’ sins, and our children suffer for ours. However, we are not responsible for their sins nor are our children responsible for ours. That is, we do not “pay” for the sins of our parents. We each stand alone before God. We each need a Redeemer and Savior (1) of our own. Furthermore, we need to forgive (1) our ancestors renouncing their sins and repenting of our own to be free from suffering caused by generational curses.