You are doing 3 things wrong:
You are patching the wrong location. You need to patch the yyyy.Client global, because that's how you imported that name.
The code-under-test is not calling Client(), it uses a different method, so the call path is different.
You are calling the code-under-test outside the patch lifetime. Call your code in the with block.
Let's cover this in detail:
When you use from xxxx import Client, you bind a new reference Client in the yyyy module globals to that object. You want to replace that reference, not xxxx.Client. After all, the code-under-test accesses Client as a global in it's own module. See the Where to patch section of the unittest.mock documentation.
You are not calling Client in the code. You are using a class method (.get_client_auth()) on it. You also then use the return value as a context manager, so what is assigned to client is the return value of the __enter__ method on the context manager:
with Client.get_client_auth(token) as client:
You need to mock that chain of methods:
with patch('yyyy.Client') as MockClient:
context_manager = MockClient.get_client_auth.return_value
mock_client = context_manager.__enter__.return_value
mock_client.get.return_value = response
result = foo(1,self.token)
You need to call the code under test within the with block, because only during that block will the code be patched. The with statement uses the patch(...) result as a context manager. When the block is entered, the patch is actually applied to the module, and when the block exits, the patch is removed again.
Last, but not least, when trying to debug such situations, you can print out the Mock.mock_calls attribute; this should tell you what was actually called on the object. No calls made? Then you didn't patch the right location yet, forgot to start the patch, or called the code-under-test when the patch was no longer in place.
However, if your patch did correctly apply, then MockClient.mock_calls will look something like:
[call.get_client_auth('token'),
call.get_client_auth().__enter__(),
call.get_client_auth().__enter__().get('some/api/path', {'param': 'value'}),
call.get_client_auth().__exit__(None, None, None)]