Ouya was apparently discontinued in 2015, I'm surprised it's still in any kind of use!
So long as it uses the standard gamepad spec it should work with the existing gamepad plugin, but I guess being 7 years out of date means it's way behind on supporting that. I'm sure you'll run in to loads of similar problems if it's that far out of date.
It's very much our intention not to expose the built-in plugin/behavior code in C3. In C2 it was not meant to be used, but people found it in the install directory and so started making tweaks, which we never wanted to happen because it causes appalling compatibility nightmares, and that's exactly what happened. It will cause more problems than it solves. If you want to do something custom, write a new plugin or use JavaScript coding.