Punishment β Is a Katan punished for transgressing a Mitzvah:[1] A child is not given any form of punishment by a human court or Heavenly Court for any sin he commits. However, some Poskim[2] rule that once a child has reached the age of understanding what is a Mitzvah and Aveira, Onas Hapeutos, he is punished in heaven for his sins, after he passes away. Furthermore, according to all, a child can be punished for the sins of his father.[3]
[1] See Halacha 10 and Toras Hakatan Chapter 39:1-28
[2] Noda Beyehuda Tinyana Y.D. 164, brought in Pischeiy Teshuvah Y.D. 376:3
[3] Rambam Teshuvah 6:1