I am migrating our code from Google Contacts API to Google People API as Google Contacts API will be deprecated soon, but I noticed new People APIs are simple to compare with the old Contacts API.
How I can find a contact for a specific group?
f.e. getContactByGroupId
Assuming that you meant getContactGroupById instead of getContactByGroupId, you can retrieve a specific contact group in People API by calling:
In this case, you have to provide the resourceName instead of the contact id. If you don't know how to get the former, consider taking a look at this answer.
If you are using Apps Script, you can enable the Advanced People Service and do something like this:
People.ContactGroups.get(resourceName);