What is the Jews’ belief concerning the return (raj’ah) of Imam Mahdi (a.s.)?
Similar to other faiths and people, the Jews definitely believe in the coming of a savior at the end of time. In the current Torah, there are many glad tidings of the coming of a universal reformer. In the Psalms of David titled “Mazamir”, among the books of the Old Testament, various promises are mentioned in this regard. What is interesting is that the Quran quotes the Psalms of David when speaking of the coming of Imam Mahdi (aj) a, and the exact same excerpt can be found in the current Torah today without any distortion. As shall be mentioned later on, Imam Mahdi’s name has not been explicitly mentioned but there are some signs which could be applied to him.
“Raj’ah” literally means to return  and in Islamic terms, it refers to the return of certain people (pure believers and absolute polytheists) from the dead before the Day of Resurrection. When it comes to Imam of Time (aj), raj’ah technically does not apply to him. Raj’ah in the question actually implies the reappearance of Imam Mahdi (aj). All the nations and peoples of the world despite their differences in thought, manners, customs, tendencies, interests, wishes and schools are interested in peace and justice. Almost all those who have studied about saviorism and the coming of a global reformer agree that the entire nations of the world are waiting for a great leader to come. Each nation uses a special name to refer to him. Therefore, the belief in the reappearance of a great savior is an old one common to all religions and nations of East and West. 
Belief in the Reappearance of a Savior among Jews
Belief in the coming of a savior exists among all nations, more pervasively and strongly among the Jews. Similar to other faiths and people, the Jews definitely believe in the coming of a savior at the end of time. In the current Torah, there are many glad tidings of the coming of a universal reformer.
As shall be mentioned later on, Imam Mahdi’s name has not been explicitly mentioned but there are signs which could be applied to him.
In the Psalms of David titled “Mazamir”, among the books of the Old Testament, various promises are mentioned in this regard. What is interesting is that the Quran quotes the Psalms of David when speaking of the coming of Imam Mahdi (aj), and the exact same excerpt can be found in the current Torah today without any distortion. Verily, before this We wrote in the Psalms (of David), after the Message (or advice given to Moses before David): My servants the righteous (the friends and companions of Imam of Time), shall inherit the earth (they will prevail it)." 
The Psalms of David say: “Refrain from anger and turn from wrath; do not fret - it leads only to evil. For evil men will be cut off, but those who hope in the LORD will inherit the land.” 
The book of Haggai says:
“For thus saith the Lord of hosts; Yet once, it is a little while, and I will shake the heavens, and the earth, and the sea, and the dry land; And I will shake all nations, and the desire of all nations shall come: and I will fill this house with glory, saith the Lord of hosts. The silver is mine, and the gold is mine, saith the Lord of hosts. The glory of this latter house shall be greater than of the former, saith the Lord of hosts: and in this place will I give peace, saith the Lord of hosts.” 
Also, the book of Daniel says: “…And at that time shall Michael stand up, the great prince whichstandeth for the children of thy people… And many of them that sleep in the dust of the earth shall awake…” 
The books of Zechariah, Amos and Ezekiel have also mentioned this matter and given glad tidings. 
The belief in the reappearance of a savior is so strong and pervasive among the Jews that the history of Judaism makes mention of people who make false claims of saviorism. Amongst the pseudo claimants, one was ShabtaiSebbi” the founder of Dunmah sect who was born in Turkey in 1626. The Jews who had suffered a lot of pain and hardship before his rise accepted his invitation and gathered round him. 
Some of the devotees of the Jewish mystic, ManachemMundelSchnerson, also believed that he was the promised Messiah and he will rise up one day. The death of this messiah at the age of 90 was very disturbing for his devotees. 
Interestingly, after the coming of Prophet Jesus (a.s.), who had a lofty divine personality, most of the Jews refused to accept him.
The Messiah that the Jews are waiting for:
Based on some texts, it seems like the one Jews are waiting for has the name of “Christ”, just like the Christians. Although this could have been considered a theory before Jesus, but such a viewpoint regarding the savior at the end of time is false, because their promised one is named “Moshiach”. This name used to be the title of the rulers of the Israelite. Since the term Christ only refers to Jesus, Jewish thinkers use the Hebrew term “Moshiach” which is translated as “Messiah”. 
The most important messianic glad-tiding has come in Isaiah wherein it says: “A sapling from the trunk of Jesse (David’s father) will come… God’s spirit will be blown into him… he will judge the indigent with justice and the oppressed with truth… the wolves will live together with lambs and leopards will sleep together with the goats…” 
The interpretation “trunk of Jesse” is applicable to many prophets including David, Solomon, Jesus and Imam Mahdi (aj). As for Imam Mahdi (aj), he is linked to Jesse’s granddaughter through her mother, Lady Narjis. b
Therefore, the Jews are awaiting the reappearance of the savior of the end of time , even though they may not have a particular person into consideration.
 Anbiya: 105.
 FarhangeMo’in, vol. 2, p. 1640.
 MakaremShirazi, Nasir, The Global Government of Hazrat Mahdi (aj), Qom, Nasl-e Jawan Publications, 11 edition, p.51,
 The Old Testament, Psalm 37, quoted from: MujtabaTune’i, Mow’udNameh, p. 230.
 Haggai 2:6-9, quoted from Mow’udNameh, p. 230.
 Daniel 12:1-12, quoted from Mow’udNameh, p. 232.
 FarhangeAlefBai, Mahdaviyat, pp. 231-232.
 Toufiqi, Hussein, AshnayeebaAdyaanBuzurg, pg. 119, Samt Organization, Tehran, 1386.
 AshnayeebaAdyaanBuzurg, p. 125.
 Ibid, p. 121.
 Torah: Isaiah, chap. 11. P.10
 Maw’udNameh: p.230.
 Today, both the extremist pro-Zionist ‘Gush Emunim’ and the extremist anti-Zionist ‘Naturi Karta’ eagerly await the coming of the Messiah.