As far as I know, the right pronunciation is with the "Z" sound, irrespective of the accent.
Even better: ey-zhuh
Refer the link: Asia | Define Asia at Dictionary.com
eisha or eija ?
Which is AmE and BrE?
According to PhoTransEdit 1.5;
BrE -- ˈeɪʤə
But according to Collins English Dictionary (via Dictionary, Encyclopedia and Thesaurus - The Free Dictionary), it is pronunciated as ˈeɪʃə and ˈeɪʒə, which are the only versions I have heard 'til now.
( ʃ-shine / ʒ - genre)
I would pronounce it ˈeɪʒə
That's the only way I've heard so far also.