I am trying to fetch the count of vCore assigned to the existing apps deployed in Mule Runtime Fabric either directly from Mulesoft or from Elastic monitoring by building the Mule Api and fetching the vcore information from it.
Did not find any document related to fetching vcores of the deployed API's in runtime fabric or on-prem.
A vCore is a unit of compute capacity for processing on CloudHub and CloudHub 2, which is equal to one virtual core. Runtime Fabric uses the concept of vCPU instead, which may be calculated differently. If by on-prem you refer to a standalone Mule runtime, it doesn't use either, since it is deployed to your own infrastructure which is not managed by MuleSoft. It may be using physical CPU cores or virtual cores in a virtualization environment however since it is not managed by MuleSoft it is up to you.
Mule applications are sometimes called Mule APIs depending on when the application implements some API. They do not report any kind of resource information unless you developed that functionality inside the application.
On the other hand MuleSoft provides REST APIs for managing applications and other Anypoint Platform services. Runtime Manager REST API provides details about a deployment that maybe useful to you. See the documentation for the endpoint at https://anypoint.mulesoft.com/exchange/portals/anypoint-platform/f1e97bc6-315a-4490-82a7-23abe036327a.anypoint-platform/amc-application-manager/minor/4.0/console/method/%231290/.
Documentation for other platform REST APIs is available on the Developer Portal: https://anypoint.mulesoft.com/exchange/portals/anypoint-platform/