Jesus clearly represents the seed of the woman who’s crushing the Serpent, and his children are clearly set in opposition to the children of the Serpent. If John is describing the outworking of Genesis 3:15, then he appears to understand the seed of the woman in that verse in both an individual and a collective sense.

The past 30 years have provided something of a renaissance in the interpretation of Genesis 3:15, with many evangelical scholars providing sound exegetical and theological argumentation that this verse explicitly anticipates a future individual offspring of the woman. However, many scholars still strongly affirm the collective understanding of the seed of the woman.
Another view proposes that the expectation of the seed of the woman is both individual and collective. In this interpretation, the verse anticipates (1) an individual coming Deliverer who will be at enmity with and exchange blows with the Serpent and (2) a collective group associated with the individual coming Deliverer who will participate in this enmity against the Serpent and his seed.
Several New Testament passages allude to Genesis 3:15 and demonstrate a collective and individual application of its outworking. Here are seven examples.
1.  Opponents of Jesus as Offspring of the Serpent
The Gospel accounts display an ongoing enmity: Jesus and his followers (seed of the woman) on one side and Satan and his agents (seed of the Serpent) on the other. On several occasions, Jesus identifies his opponents as children or offspring of the Devil. In attributing their spiritual parentage to the Devil, Jesus declares his opponents are thinking and acting like the Devil.
Jesus directly addresses the Pharisees as “serpents” and a “brood of vipers” (Matt. 23:33; cf. 3:7; Luke 3:7). A Jew identifying someone as the offspring of a serpent is, in view of the broader context of the Old Testament, quite possibly alluding to Genesis 3:15 to some degree. These statements don’t necessarily address whether the seed of the woman is individual or collective, but they do suggest Jesus understands his opponents to be representative of the offspring of the Serpent.
In John 8, Jesus identifies the Jewish religious leaders with the offspring of the Serpent in his heated dialogue with “the Jews” (also identified as the Pharisees in v. 13) who insist they’re the offspring (σπέρμα) of Abraham (vv. 33, 39). Though Jesus concedes these “Jews” are offspring of Abraham in a physical sense (v. 37), they’re not truly “Abraham’s children” (τέκνα τοῦ Ἀβραάμ) because they don’t do “the works Abraham did” (v. 39).
True offspring of Abraham wouldn’t seek to kill Jesus, a man who speaks God’s truth (vv. 37, 40). Furthermore, God cannot be their father (v. 41) since they’re rejecting Jesus, the One whom God had sent (v. 42). Instead, the Devil is their father, since they fulfill his desires in their opposition to Jesus (v. 44).
Jesus points out the two primary sins of the Devil that solidifies their connection to him: he was a “murderer from the beginning,” and he is “a liar and the father of lies” (v. 44). The Jews’ intent to murder Jesus (vv. 37, 40, 44, 59), their rejection of his truth (vv. 37, 43–47), and their propagation of lies (vv. 41, 48, 52) demonstrate their character reflects the character of the Devil. The Devil, then, is their spiritual father, and they’re his offspring.
Because Jesus is certainly alluding to the Serpent’s actions in Genesis 3 in identifying the Devil as a liar and a murderer, he’s likely thinking of that chapter in referring to the unbelieving Jews as children of the Devil—the offspring of the Serpent.
“Enmity” describes Jesus’s relationship with such offspring of the Serpent. When Jesus confronts the offspring of the Serpent, he doesn’t come peaceably; rather, he engages in a harsh war of words in which he identifies and overcomes the agents of Satan.
This enmity doesn’t end with the Serpent’s seed’s rejection of Jesus; it continues with the offspring of the Serpent persecuting, flogging, killing, and crucifying Jesus’s messengers (Matt. 23:34–35). If these entities are representative of the offspring of the Serpent and if they’re at enmity with the individual Messiah, then these references appear to support the idea of the individual offspring of the woman being fulfilled in Jesus. Jesus presents these as enemies not only of himself but also of his followers. Therefore, throughout Jesus’s ministry, the offspring of the Serpent are at enmity with Jesus and his followers. 
Though Jesus’s followers aren’t specifically identified as “offspring of the woman,” their position of enmity with the offspring of the Serpent assumes this identification. It isn’t necessary for Jesus to say, “You, my disciples, are offspring of the woman” in order to understand that the theme of enmity promised in Genesis 3:15 is being displayed in the Gospels. These conflicts support the idea of enmity between both individual and collective offspring.
2.  John’s Theology of the World (Gospel of John)
John’s theology of the world also reflects the individual and collective enmity between the seed of the woman and the seed of the Serpent. John presents Satan as the ruler of the world (John 12:31; 14:30; 16:11; 1 John 5:19), who works in direct opposition to Jesus. The “world” in this sense in John refers not to the created universe but to the sinful people and the systems that stem from those sinful people (and from their ruler, the Devil).
John positions the world in direct opposition to Jesus. Not only does the world hate Jesus (John 7:7; 15:18–24), but the world also hates believers—those who follow Jesus (John 15:18–24; 17:14; 1 John 3:13).
If Satan is identified as the Serpent from Genesis 3, and those who follow after him are identified as his “seed” or his children (or “the world”), then it seems consistent to understand John’s theology of the world as unfolding the concepts presented in Genesis 3. Satan and the world persist in their enmity toward Jesus and believers. The world “hates” Jesus and his people. Satan and the sinful leaders of this world put Jesus to death (striking his heel), but Jesus ultimately is victorious over the Devil (striking his head) and overcomes the world (John 16:33). Christians participate in this victory as they also overcome the world (1 John 2:13–14; 4:4; 5:4–5).
Though John doesn’t specifically identify believers as “offspring of the woman,” he clearly states they’re at enmity with the Devil and those who follow the Devil.
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