I'm not sure exactly what you are trying to achieve?
If you need to allow users to attach a twitter account to your system, and every mention of this user about a new support ticket, this is really possible. You will need to look at the Twitter API documents.
https://dev.twitter.com/overview/documentation
In particular, look at mentions_timeline. From here, for each tweet you are looking at, for a specific user you can create a new ticket. You could further improve the logic by making sure that you did not register tickets for answers, etc., to make sure that you are not repeating registration incidents.
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