The Veterans Fellowship Act directs the Assistant Secretary of Labor for Veterans' Employment and Training to implement a pilot program focused on short-term fellowship opportunities for veterans. This initiative allows selected states to utilize existing grant or contract mechanisms to establish these programs, fostering partnerships with non-profit organizations to execute the fellowships. Each short-term fellowship program will enable veterans to participate with an employer for a period not exceeding 20 weeks, providing them with a monthly stipend during their participation. A key objective of these fellowships is to offer veterans a direct pathway to potential long-term employment with the participating employer upon completion. The bill authorizes an additional $10,000,000 annually for fiscal years 2025 through 2029 to support this pilot program, and requires a Comptroller General report on its effectiveness within four years.