In Slovak it sounds like Jašoviec with emphasis on the first syllable : Jašoviec. You read it the same way as in Polish, but accent is different, of course. You can find Jašov- toponymy in Slovakia as well, e.g. Jašov vrch (Jašov peak). Moreover, I found a surname Jašovec among Slovaks in Vojvodina, but I'm not sure whether it's South Slavic influence or they 'brought' it from Slovakia.