hey,
i am not enrolled in a psyd program, but I know the psyd @ Rutgers offers some fellowships. Your best bet for a fellowship directly through a university would be through an established university. I have heard that Baylor in texas has a strong clinical psyd, so that may be another program to look into. Most psyd students self-finance, as most psyds are through for-profit institutions (at least that is my understanding). there are fellowships outside of university, but you generally have to have some track record of research before you will be competitive for them.
Good luck!