What is the basis for the belief that the name of the Messiah is יָהוּשׁוּעַ (Yahushua)? There are some1 who assert that the name of the Messiah is יָהוּשׁוּעַ (which would be transliterated into English as Yahushua). What is the basis for this assertion?

Note: The question is not asking about the name יְהוֹשׁוּעַ but a slight variation of that name, viz. יָהוּשׁוּעַ, which certain people believe is the actual name of the Messiah, as opposed to יְהוֹשׁוּעַ.

1 See Google search for the word "Yahushua."
It stems back to Leah calling her 4th son "Judah".  Well, there are no "J's" in Hebrew, which would then bring Judah to Yudah[their letter Yod/Y was converted to J in modern translations].  This Yod/Y is represented as a little apostrophe[the smallest of the Hebrew letters]; you'll notice it above to the right of that Hebrew word for Yahushua. Well Yudah is actually a shortened down form/word that was originally Yahudah.  If we break down Yudah or Yahudah, we get[basically] Yah and dah.   Yah is what He was called according to Psalm 68:4; and dah means praise...We see this in Gen 29:35.  If we take just the Yah or Yahu portion of Judah, and add "shuah", we end up with Yahushua.  Why do we add shuah?  Shuah is Hebrew for Salvation/Saviour.  Jesus could not possibly be enunciated with a "J" sound in Israel 30AD because their alphabet wouldn't allow it.  We look at the scriptural renditions of His appellation and attempt to more closely render an English spelling to a Hebraic word uttered years ago; this is called transliteration.  Additionally, there is a reliance upon the veracity of the Grecian copies of the original scripts, thus assertion is made that "Yahushua" is the gem.