Hi that is an interesting question Do children pay for the sins of the parent? The answer is no children do not even think this way, it is human nature for parents to make the child feel so. Perhaps this is done so the parent can have the children suffer with them, so they won’t be alone. Whatever the situation may be children are not at all responsible in any way for sins related to our parents. It is true that the child may be a result of a sin committed by a parent but that does not mean anything. So, we have to now consider that parents have made a wrong move by involving the children into their lives.
On the other hand, a child may commit the same sin as their parents this may be because of circumstances or environment that led to the same conditions that the parent was already in. It may also be a result of how the child had the very same personality of the parent and committed the same mistakes that the parent did. In summing up all the conditions that lead to whatever matter it is not the way of the Lord to hold a child responsible for the sins of the parents.
Galatians 6:3-5
Modern English Version (MEV)
3 For if someone thinks himself to be something when he is nothing, he deceives himself. 4 But let each one examine his own work, and then he will have rejoicing in himself alone, and not in another. 5 For each one shall bear his own burden.