The very short answer is: No, Jews do not believe in the Devil of Christian theology.
A longer, more complete answer:
Jewish scripture has a character known as HaSatan, the Adversary. HaSatan appears in the beginning of the Book of Job:
One day the divine beings presented themselves before the LORD, and the Adversary came along with them.
The LORD said to the Adversary, “Where have you been?” The Adversary answered the LORD, “I have been roaming all over the earth.”
The LORD said to the Adversary, “Have you noticed My servant Job? There is no one like him on earth, a blameless and upright man who fears God and shuns evil!”Job 1:6-8
In this and in chapter 3 of the book of Zachariah, “HaSatan” is not a personality. HaSatan is the title of a role, a job description. “Ha” means “the.” “Satan” means “adversary.” In Job, HaSatan plays the persecutor, taunting God that Job only loves God because God has been good to him. God allows HaSatan to inflict suffering on Job so that Job can demonstrate his faith in God. In Zachariah, he is the Accuser, and an angel (malach) is God’s mouthpiece, rejecting the accusations of HaSatan.
The figure in the adversary role has little or no volition: it cannot do anything without the permission of God. It plays a role equivalent to that in English of a “devil’s adversary:” it is an expression of opposition. Angels have a similar role in the Jewish Bible: they function as messengers or as extensions of God, but they do not have agency of their own.
Sometimes in other texts HaSatan is an expression of the yetzer harah, the evil or selfish inclination. It never acquires the independence, to say nothing of the raw power, of the Satan figure in Christian tradition.
There are a number of Talmudic texts about HaSatan, for instance:
Reish Lakish says: Satan, the evil inclination, and the Angel of Death are one, that is, they are three aspects of the same essence. He is the Satan who seduces people and then accuses them, as it is written: “So the Satan went forth from the presence of the Lord, and smote Job with vile sores” (Job 2:7). He is also the evil inclination, as it is written there: “The impulse of the thoughts of [the human] heart was only evil continuously” (Genesis 6:5); and it is written here: “Only upon [Job] do not put forth your hand” (Job 1:12). The verbal analogy between the various uses of the word “only” teaches that the evil inclination is to be identified with the Satan. He is also the Angel of Death, as it is written: “Only spare his life” (Job 2:6); apparently Job’s life depends upon him, the Satan, and accordingly the Satan must also be the Angel of Death.Bava Batra 16a
HaSatan has these roles (a named figure in Job, the evil inclination in humans, and the Angel of Death) as it is picked up as a theme in Jewish mystical writing and in folklore, but it is in those sources that it takes on a role more like that of the Christian Satan. That may be from cross-pollination of Jewish and Christian ideas in golden-age Spain and in northern Europe. It may also have arisen from the need of a suffering people to separate the suffering in life from the all-good person of their God.
At any rate, most modern Jews do not believe in “Hell” and do not believe in “Satan” as an independent figure busy in the world. We are much more inclined to attribute the evils that come from human misbehavior to human beings, and to attribute “evils” from the natural world (earthquakes and other natural disasters) to the balance of nature established by God.
Jews have been and continue to be ferociously monotheistic, so that an independent and equal opponent to God is a logical impossibility.
What do you believe, and why?