This was one of the themes in The Count of Monte Cristo. Edmond Dantes (Monte Cristo) in revenging his conspirators mentions this as a biblical statement. Does the bible really believe that the son bears some responsibility for his father's deeds?
The Bible understands generational culpability writ large, as in corporately, but not individually.
In other words all men are dead in sin, because all men were represented in Adam (Romans 5:12) and nations as nations are responsible before God, and individuals may suffer the consequences of that corporate evil. (Jeremiah 16:11-13).
However, I am not responsible for my father's sins. (Ezekiel 18:20).