It is my understanding that the word parasite is spelled with an i and not a y. However, the title of the anime and manga, when translated into English, uses a y in the spelling.
However, this only seems to apply to the title, since the species is referred to as "parasites" (at least throughout the wikipedia article) and Uda Mamoru calls his parasite as Parasite in episode 7:
Is there a reason for this misspelling?
Or is there maybe a difference between "parasyte" and "parasite"?