You labelled this with Cloud but then said Server in the question. Jira server has an internal API you can use in apps. Both server and Cloud have (similar, but not the same) REST APIs.
Whichever one of those three you might be looking for, there's a starting point at https://developer.atlassian.com - select the Cloud or Server tab and then look to the "Jira Software" tab, as Sprints are a Software artifact.
Connect with like-minded Atlassian users at free events near you!Find an event
Connect with like-minded Atlassian users at free events near you!
Unfortunately there are no Community Events near you at the moment.Host an event
You're one step closer to meeting fellow Atlassian users at your local event. Learn more about Community Events