It is possible integrate github with a custom application that track issues? This custom issue tracker is developed by people that is not involved with github development, but can code some plugin or feature that provides a pattern to refer a external issue.
The pattern can be #I or something like this.
Thoughts?
As far as I'm aware, most popular enterprise solutions are building integrations with GitHub repositories via webhooks (if they don't already offer them). If this is a in-house custom solution you will have to build that integration yourself.
You'll need to register a webhook for each repository and you will have to know how to associate events from different repositories with different issues.
With the webhook set-up you'll be able to inspect pull requests, pushes to different branches, etc. and you can use whatever syntax you want to refer to issue ids in your issue tracker. If your repository is also public facing and has issues (and pull requests) turned on, you will definitely not want to overlap usage of #numerical_id with your own issue tracker. In that case, you will want to choose something like ^ or & or % which isn't currently claimed by anyone else. What you choose for that, though, is entirely up to you.