Xray uses Jira issues for implementing Test, Pre-Condition, Test Set, Test Execution and Test Plan entities. Therefore, these entities may be created or updated using Jira's native REST API, based on Jira authentication.
Xray itself provides a REST API, with endpoints specifically made for dealing with test management.
Requests made to Xray's REST API must be authenticated using a client id and a client secret, which in turn are based on an API Key created for some user in Xray Global Settings: API Keys global settings.
Thus, the first step you need to do is obtaining a token based on the Client Id and Client Secret of your assigned API Key. From thereon, you can use it to make whatever requests to Xray Cloud.
Feel free to contribute!
Xray is used and integrated with many different platforms, so if you have the time and know-how, feel free to contribute an API implementation in your preferred language (e.g., Java, .NET, JavaScript, etc). We'd be happy to include links to your contribution 