First, please check if you are using Xray on Jira cloud or Jira server/datacenter.
To submit results from Jenkins you have 3 options:
- use the Xray Jenkins plugin UI itself, and configure a project to submit the test results; this is pretty straighforward
- use the Xray Jenkins plugin but from the pipeline; for that you need to generate the pipeline script
- use either the Jenkins UI or the pipeline to invoke the API by hand; for this you don't need the Xray Jenkins plugin, you just need some tool such as "curl" to perform the HTTP requests (see example for GitLab and Xray cloud here, and for Xray server/DC here)
Note that for Xray in Jira cloud, you need to use client_id and client_secret to perform an initial authentication request (in case you're doing the requests by hand). These are obtained from an API key defined on Xray global settings.
For Xray on Jira server/datacenter, you may use Jira credentials (e.g. Jira username + password). It only requires you to perform one request and submit the test results.