Here are some scriptures that show the "Branch" to be the future Messiah
Jeremiah 33:15 (KJV) In those days, and at that time, will I cause the BRANCH of righteousness to grow up to David; and he shall execute judgment and righteousness in the land.
16 (KJV) In those days shall Judah be saved, and Jerusalem shall dwell in safety: and this [is the name] by which she shall be called, Yahweh our righteousness.
Isaiah 11:1-AV And there shall come forth a rod out of the stem of Jesse, and a BRANCH shall grow out of his roots:Here is Yahushua's name prophesied
2 (KJV) And the spirit of Yahweh shall rest upon him, (see John 1:32) the spirit of wisdom and understanding, the spirit of counsel andmight, the spirit of knowledge and of the fear of Yahweh;
3 (KJV) And shall make him of quick understanding in the fear of Yahweh: and he shall not judge after the sight of his eyes, neither reprove after the hearing of his ears:
4 (KJV) But with righteousness shall he judge the poor,and reprove with equity for the meek of the earth: and he shall smite the earth with the rod of his mouth, and with the breath of his lips shall he slay the wicked.
5 (KJV) And righteousness shall be the belt of his loins,and faithfulness the belt of his reins.
Jeremiah 23:2-AV Therefore thus saith Yahweh Elohim of Israel against the shepherds that feed my people; Ye have scattered my flock, and driven them away, and have not visited them: behold, I will visit upon you the evil of your doings, saith Yahweh.
3 (KJV) And I will gather the remnant of my flock from all countries where I have driven them, and will bring them again to their folds; and they shall be fruitful and increase.
4 (KJV) And I will set shepherds over them who shall feed them: and they shall fear no more, nor be dismayed, neither shall they be lacking, saith Yahweh.
5 (KJV) Behold, the days come, saith Yahweh, that I will raise to David a righteous BRANCH, and a King shall reign and prosper, and shall execute judgment and justice upon theearth.
6 (KJV) In his days Judah shall be saved, and Israelshall dwell in safety: and this [is] his name by which he shall be called, YAHWEH OUR RIGHTEOUSNESS.
7 (KJV) Therefore, behold, the days come, saith Yahweh, that they shall no more say, Yahweh liveth, who brough tthe children of Israel out of the land of Egypt;
8 (KJV) But, Yahweh liveth, who brought and who led the seed of the house of Israel out of the north country, and from all countries where I have driven them; and they shall dwell in their own land.
Zechariah 3:8-AV Hear now, O Joshua the high priest, thou, and thy fellows that sit before thee: for they [are] men wondered at:for, behold, I will bring forth my servant the BRANCH.
Joshua is pronounced Yahushua in the original Hebrew because Hebrew has no "J" or "J" sound
Zechariah 6:9 (KJV) And the word of Yahweh came to me, saying,
10 (KJV) Take of [them of] the captivity, [even] ofHeldai, of Tobijah, and of Jedaiah, who are come from Babylon, and come thou the same day, and go into the house of Josiah the son of Zephaniah;
11 (KJV) Then take silver and gold, and make crowns, and set [them] upon the head of Joshua the son of Josedech, the high priest;
So the Scripture is saying: "Behold (or look) the man (Yahushua) whose NAME is the BRANCH!" Therefore the current High Priest of Judah in the days of Zechariah Joshua (Yahushua) has the name of the "BRANCH" or the coming Messiah.
Zechariah 6:12 (KJV) And speak to him, saying, Thus speaketh Yahweh of hosts, saying, Behold the man whose name [is] The BRANCH; and he shall grow up out of his place, and he shall build the temple of Yahweh: