Our approach to test a product that contains an API
Understand that API Testing is a testing activity that requires some coding and is usually beyond the scope of what developers are expected to do.
Traditional testing techniques such as equivalence classes and boundary analysis are also applicable to API Testing.
It is almost impossible to test all possible scenarios that are possible to use with your API. Hence, one should focus on the most likely scenarios, and should also apply techniques like Forced Error Testing using different data types and size to maximize the test coverage.