Jehovah's Witnesses like to point out the Bible refers to Satan as "the god of this world" (II Corinthians 4:4). And, as far as that goes, they are correct, though their application of that verse is self-serving and exegetically-unwarranted. Paul is obviously referring to this world spiritual system, not this world as the totality of everything.
The problem is that there are a lot of other things said about Satan, that the Jehovah's Witnesses (and a lot of other people) don't address.
Consider Luke 11:21:22: "When a strong man, fully armed, guards his own palace, his goods are safe; but when one stronger than he attacks him and overcomes him, he takes away his armor in which he trusted and divides his spoil." In its context, Jesus had cast a demon out of a man who was deaf-mute. The Pharisees claimed that He had done this by the power of Satan, the ruler of demons. The response of Jesus was to compare His actions to those of a burglar, who would first bind the master of a house, before pillaging the house of its goods. While we may be uncomfortable with Jesus's using a thief as an analogy for Himself, His meaning is clear. He wasn't acting by the power of Satan. Rather, He had bound Satan's power, and was now pillaging Satan's kingdom of its spiritual goods, those in bondage to his control.
Next consider John 1:31: "Now is the judgment of this world; now will the ruler of this world be cast out." Jesus said this immediately after the Father had announced verbally that Jesus was His divine Son. Thus, His coming into the world was a strike against the power of Satan. Think of the demolition of a building. Explosives are set at strategic points in the building, and then blown. the building doesn't collapse all in a single swoop. Rather, sections collapse in an orderly series into each other. This statement of Jesus doesn't indicate a single, catastrophic collapse of Satan's power, but rather a step in its systematic destruction.
We can confirm that interpretation with another verse, John 16:11: "The ruler of this world is judged." Jesus describes Satan in language equivalent to that of Paul. However, this ruler isn't basking in his power, for he has been judged. His destruction has been determined, and his overthrow has been initiated.
Paul repeated that assurance in Colossians 2:15: "He disarmed the rulers and authorities and put them to open shame, by triumphing over them in Him." In His ministry thus far, i. e., everything from His incarnation to His ascension, had all served to undermine and overthrow the spiritual powers that had dominated the nations. Thus, when Paul described Satan as "god of this world" in one passage, it was with the understanding that he expressed in this passage, that Satan may be the head of the humanistic worldview that is opposed to God, but that worldview and headship have been defeated in Jesus Christ!
Satan is defeated, and his ultimate state has been determined (Matthew 25:41). See also Revelation 12:8-9, Luke 10:18, and John 12:31. The New Testament consistently portrays Satan as an opponent of Jesus Christ, but a defeated opponent. And, as Revelation 12:12 indicates, even what influence Satan retains in his defeated state, is only for a short time.