Perhaps you should start at - https://developer.atlassian.com/display/JIRADEV/JIRA+Developer+Documentation
Then you can refer this below link to create the JIRA issue programtically-
If you mean as part of a plugin, then the other answers apply. However, if you are asking how to automate various JIRA activities for intergration with other products, the JIRA Command Line Interface is a simple option. Specifically, createIssue action. Easy to program in Java or scripting languages like groovy :).
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