what types of test should we write for apis code example

Example: testing types in api

Unit testing and Functional testing
Load testing to test the performance under load
Discovery testing to list, create and
delete the number of calls documented in API
Usability and Reliability testing
to get consistent results
Security and Penetration testing
to validate all types of authentication
Automation testing to create and 
run scripts that require regular API calls
End to end Integration and Web UI testing
API documentation testing to
determine its efficiency and effectiveness