Fratricide (from the Latin words frater "brother" and cida "killer," or cidum "a killing," both from caedere "to kill, to cut down") is the act of killing one's brother.

It can either be done directly or via use of either a hired or an indoctrinated intermediary (an assassin). The victim need not be the perpetrator's biological brother. In a military context, fratricide refers to a service member killing a comrade.

Judeo-Christian religion recognizes the biblical account of Cain and Abel, this fratricide was the first type of murder to be committed. In the mythology of ancient Rome, the city is founded as the result of a fratricide, when the twins Romulus and Remus quarrel over who has the favor of the gods and over each other's plans to build Rome, and Romulus becomes Rome's first king and namesake after killing his brother.

The terms used for the other answers are shown below:

The killing of one's father is called patricide.

The killing of one's mother matricide.

The killing of one's own sister sororicide.

More Info: en.wikipedia.org