When reading this, be sure to remember that not all countries see children as having any rights at all. The answer is written based upon American rights for children of inmates as denoted by the "Children of Incarcerated Parents Bill of Rights."
Much like the more historically known Bill of Rights, the "Children of Incarcerated Parents Bill of Rights" givens children certain rights based upon their status as the child of an incarcerated parent/s.
A paraphrase of these rights are as follows:
Children of incarcerated parents have the right to be kept safe, cared for and have support (meaning medical/psychological).
Children of incarcerated parents have the right to be informed regarding their parent/s incarceration.
These children have the right to give testimony which can be considered when it comes to their parent/s future.
These children have the right to be able to see, speak with, and have physical contact with their incarcerated parent/s.
These children have the right not to be judged based upon their parent/s mistakes.