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Only the latter can also be spelled apophansis, though.
I presume the word (which has not yet made it into the OED) is based on Greek apophaino 'show forth, display' and thus represents a hypothetical *apophainia (the actual Greek derived nouns are apophansis and apophasis), so that the proper UK spelling would be "apophaenia" (though googling that form turns up only a page from a Russian medical dictionary giving it as the etymon of Russian apofeniya; a nice question is whether that can be considered a correct etymology).