Ordinarily I would say that your name means whatever was the intention of the person who gave you that name -- regardless of spelling variations.
However, you are in luck, Jasika! A 'net search revealed that the word "jasika" is Slavic for "aspen tree":
http://www.rastko.org.yu/projekti/kodovi/kodovi_eng.html
Even cooler, the website goes on to explain that "myths concerning aspen origin are... connected with the Devil." I'm going to make a note of "Jasika" now, and add it to my list of favorite names! (Hey, Priapos & Daividh, it even has six letters!)
So now you can tell people that your name really does mean something, exactly as it is spelt. :)
-- Nanaea