I am a father and my son's age is only 6 months. Right after becoming father I use to be concern on the matter of the liability of the parents. Because I must be liable to Allah on the day of judgment about the mistakes/sins of my child. I will be questioned did I properly guide my children in duniya? So what Islam says about this? Even if I teach my child all the basics of islam, akhlaq, etc. will I be liable of the sins/faults of my child?

If you did your job, teaching them the good deeds, and set an example for them, then you are not responsible for what they do.