I have read that parent's sins affect their children also, but my question is different/opposite, which is- Is the punishment of any individual's sin will be carried by that individual only or his/her deeds can affect other family member also? Will they also be responsible for his/her sins? Reference from Bhagavad Gita or vedas will be appreciated.
Many a times in Hinduism scriptures we find the mentioning the fact that an individual is solely responsible for his own actions/deeds/good or bad karmas ,and no one can inherit his deeds or they can not be transferred to another person or family member.
But in general it's a widespread belief with us that family members especially parents can share the wrong deeds or sins of children or wife can share the deeds of husband. So according to Hinduism scriptures good-bad deeds /sins etc. is carried by that individual only. And he and only he has to bear the fruits of his own actions.
Mahabharata - Shanti Parva - Moksha Dhama Parva -Chapter 291 - Shloka 22 .
नायं परस्य सुकृतं दुष्कृतं चापि सेवते |
करोति यादृशं कर्मं तादृशं प्रतिपद्यते ||22||
P. 347 One never has to enjoy or endure the good and bad acts of another. Indeed, one enjoys and endures the fruits of only those acts that one does oneself.
There are some shlokas we find in Mahabharata-Shanti Parva- Apaddharmanusasana Parva- SECTION CLIII. That indicate us that no family members can inherit the deeds of a individual and are pointing towards the fact that no family members are punished for his own sins of a person. The following is about the father and the next one is about family members.
न कर्माणा पितु : पुत्र : पिता वा पुत्रकर्मणा |
मार्गेणान्येन गच्छति बद्धा : सुकृतदुषुकृते ||38||
P. 337 - The son is not bound by the acts of the sire, or the sire by those of the son. Bound by their own acts, good and bad, all have to travel by this common road.
यत् करोति शुभं कर्म तथा कर्म सुदारुणं |
तत् कर्तैव समश्नाति बान्धवानां किमत्र ह ||41||
P.337 - The actor alone enjoys the fruit of acts, good or bad, that he does. What concern have kinsmen with them?
So in brief looking at above shlokas from the scripture especially Mahabharata suggests us that no family member will get punished for sins of a person , he alone will be.