module has no attribute

The problem is submodules are not automatically imported. You have to explicitly import the api module:

import myproject.mymodule.api
print myproject.mymodule.api.MyClass

If you really insist on api being available when importing myproject.mymodule you can put this in myproject/mymodule/__init__.py:

import myproject.mymodule.api

Then this will work as expected:

from myproject import mymodule

print mymodule.api.MyClass