There is one dummy API which is available for free on github. You can download it from the link given in the Helpful resources section.
API related security issues can be tested on this dummy API.
For beginners it is a very good way to understand common security issues found in APIs
You can use the POSTMAN tool for testing the TiredFul API. Link to download the tool is also given below.
You can refer to OWASP top 10 for API for better understanding of the security issues demonstrated in the dummy API.
You can also refer to the tutorial on the solutions provided in the link below.
Helpful resources: