Depending on the testing framework/tool you are using you should be able to create a test report as an output of the test execution. Those reports can be an XML, Json or other type of file and those are the files we use to import the results into Xray (check the supported format here: https://docs.getxray.app/display/XRAY/Import+Execution+Results+-+REST).
To integrate with Jenkins please check here: https://docs.getxray.app/display/XRAY/Integration+with+Jenkins, you will find explanation on how to use the plugin in Jenkins in the UI or as code to import those results back into Xray. You can find code samples here: https://github.com/Xray-App/tutorial-jenkins-pipeline for the different ways you can integrate with Jenkins.
My suggestion is to generate a test result file as an output of the test execution and import those files into Xray, this will allow you to have multiple tests executed in one Jenkins job generating multiple test results files that can imported in several API calls.