There are several good sources in your search for fellowships for which you are eligible and can be competitive. Ask your advisor and mentors. They will know about discipline-specific awards. They may even have served on review panels for the funding agency or been recipients themselves of the awards during their graduate and post-doc years.

Identify fellowships that your more advanced peers have received. (And ask them for advice and copies of their successful proposals.) As you read journal articles in your discipline, check the author acknowledgement footnotes. What sources do the authors mention for funding their research and scholarship? Check the web sites of these foundations and agencies to determine if they have graduate and post-doctoral fellowship competitions.

The most comprehensive listing of funding for graduate students is found in graduate schools’ searchable fellowship databases. With these you can search in various categories or with key words related to your discipline, field, or research topic. And these institutions allow open access to their lists:

Columbia University Graduate School of Arts and Sciences
Cornell University Graduate School
Duke University Office of Research Support
University of Chicago Graduate School
University of Michigan Rackham Graduate School
Community of Science Funding Opportunities