You want to access the External IDs from replicated Accounts and Products using the OData API V2 service -> C4CODATAAPI, but you cannot find the ExternalIDMapping collection or the navigations.
SAP Cloud for Customer.
Reproducing the Issue
Open the URL https://myXXXXXX.crm.ondemand.com/sap/c4c/odata/v1/c4codataapi/$metadata in Google Chrome, Postman tool or any other tool that works with OData REST APIs(myXXXXXX represents the URL of your C4C system).
See there is no ExternalIDMapping collection or navigation property listed in the service metadata.
You can use the ObjectIdentifierMappingCollection in C4CODATAAPI for this purpose. Here is the documentation with more details:
External ID Mapping, ExternalIDMapping, ProductCollection, AccountCollection , KBA , LOD-CRM-INT-API , OData API (C4C Only) , Problem