After researching on the topic for a considerable amount of time, it seems most of the sources which describe the Neo-Hittite Chimera, do not contain any myths about the creature nor any in-depth details.
Therefore, it leads me to believe what another source said (emphasis mine):
> "On the orthostats at Neo-Hittite sites, **the Chimaera had no narrative context and served only to ward off evil** , but in Greek myth the beast was to be conquered by a hero"
>
> source: <
Which means, the Neo-Hittite Chimera was created just to "ward off evil" and hence does not have any myths associated with it.