Creating test cases in objective-c static library with XCTest

I have a static library in objective-C that has 1 main class, which is the delegate to multiple classes and includes delegate methods to handle server calls and location updates. Since I'm developing a static library, only logic unit test is supported. I'm having a hard time coming up with test cases. I read articles on unit testing that suggests not to test private methods and constructors. I wrote basic tests like testing a async method that makes an api call and checking the delegate method's return value. What is a good starting point when creating logic unit tests for a static library?