As per this thread - same issue
I am facing the exact challenge that you were - finding the API to create a New View Version of an existing part.
I was exited to find what seems to be a "yes the API exists" but struggle a bit since I am only used to work with the REST API.
Can you provide input to whether the "Create New View Version" also exists in the REST API?
The actual answer of PTC support is that it is "Not part of Windchill PDMLink REST Services functionality".
But like you, I am very interrested to be able to do it using REST APIs
So you need to develop your own rest function
you can start here > CS183488 - Windchill PLM - REST Services Customization