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The Jasconius is a creature with origins in Roman mythology, legend and folklore. In particular, accounts of its existence first arose in Pliny the Elder's Natural History. However, the specific name Jasconius is not given for the creature until a much later account from Medieval Europe (specifically in an account called The Legend of Saint Brendan).
Or, at least, most believe that the Jasconius is first mentioned in Ancient Greek texts. However, there are some that believe the creature is first mentioned in the Bible. Specifically, they believe that the Jasconius is the gigantic fish that swallows Jonah up, for three  days and three  nights, in Jonah 2:2. Though, in all actuality, there is no evidence that the two fish are the same, other than the fact that they can both grow to enormous size.
Likewise, no source actually even gives a translation for the name 'Jasconius', or any of the name's variations. The closest one comes to any name with a distinct meaning is when Pliny the Elder refers to the creature as "pristis", meaning "of immense size". And yet, this seems more like a description than a species name.