offspring: the young a creature brings forth, used in the Gospels only in the insult "brood of vipers."
This noun comes from the verb for fathering or giving birth to someone (γεννάω), and it names the result of that act: the young a creature has brought forth. That is a slightly different idea from the ordinary word for a son or a daughter (τέκνον), which places a person inside a family. This word points back at whatever produced the young, so it always carries a claim about where they came from and what they are therefore like.
All four New Testament uses are the same two word taunt, said to people's faces: they are the young that poisonous snakes produce. John the Baptist says it to the crowds coming out to be baptized (Matthew 3:7, Luke 3:7), and Jesus says it to his opponents (Matthew 12:34, Matthew 23:33). Each time it is followed by a question about escaping judgment or about what comes out of a person's mouth, so the insult is doing an argument's work: what bred you is what you are.
The surrounding words sharpen it. In Matthew 3 and Luke 3 the phrase sits right beside a demand for "fruit worthy of repentance" (καρπός) and a warning that God could raise up children for Abraham out of the stones on the ground: the crowd claims one ancestry, and John hands them another. In Matthew 12 the same taunt introduces the rule that a tree is known by its fruit, and in Matthew 23 it is stacked on the blunter word for snakes. The picture holds steady across all four: a viper's young are dangerous before they have done anything at all, simply because of what made them.