What is the legal ruling regarding an unmarried brother committing adultery with his unmarried sister, then killing the child after its birth, and then the father killing both of them? And is the father's ruling, if he kills them, the same as one who intentionally kills a Muslim, and what is the evidence for that?

Incest is one of the most heinous major sins, and its iniquity is greater than that of fornication with a non-mahram (definition). Jurists differ on its punishment. The majority of jurists believe there is no difference between the punishment for fornication with a mahram and with a non-mahram. However, there is a weak hadith (definition) indicating that the one who commits fornication with his mahram should be killed and his property confiscated (one-fifth taken). Imam Ahmad has a narration stating that he should be killed absolutely. The authority to carry out punishment belongs exclusively to the ruler. As for killing a child after birth or killing the two fornicators by the father, it is an unlawful killing that warrants severe warning in the Qur’an and Sunnah (definition), though the majority of scholars believe that a father is not to be killed for killing his son.