(again, this is quoting Mr. Yosef, with a claim he believes he has invalidated:)
... (Yeshu'a) was a popular name at the time ...(and this is me): putting the apostrophe in Yeshua where he does is technically inaccurate. The final vowel is a furtive patach (patach genuva). Unlike most cases of this vowel, a furtive patach "steals ahead" of the letter its under (maybe that's a way to remember the hebrew name at least - "stealing patach" ;). And the ' represents the "ayin," the guttural stop which ends the name. The general rule is this: whenever the patach is under a final guttural which comes after an unchangably long vowel which is not a-class (as is the case here with the shurek, the "u" vowel in Yeshua), the patach is furtive. For a more clear example, consider the word mashiach or "anointed one," as in Yeshua HaMashiach. Though the "a" sound is under the guttural chet, which would normally mean the "a" follows the "ch," here the "ch" follows. So you say mashiach not mashicha. That's the furtive patach.
Perhaps the furtive patach goes undercover in its stealing ahead because the letter ayin, as a guttural stop, is silent. So unlike the chet in Mashiach its not obvious where the ayin actually goes when the name is spoken normally. But at any rate, if one wanted to be hardcore a completist as Mr. Yosef wants in his transliterating, one would put the guttural stop (') after the "a": Yeshua'.
(I believe this may be confirmed by any textbook on Introduction to Hebrew Grammar, and also by my rad Bible software).