Custom Object Update via REST API

Summary:

Custom Object Update via REST API

Content (please ensure you mask any confidential information):

We created a Custom Object and want to access this Custom Object via REST API. Any operation gets me a 403 - Forbidden HTTP response. I tried adding the specific custom Object privileges (CREATE,READ,UPDATE & DELETE) to the user still not able access Custom Object via REST API.

Only if the role "Custom Objects Administration" is given, then REST API access to this Custom Object is possible. We don't want to give this admin role to the user, instead give only the specific custom object privileges to access via REST API.