Topological phases of matter are featured with exotic edge states. However, the fractional quantum numbers at edges, though predicted long ago by Jackiw and Rebbi, remain elusive in topological photonic systems. Here, we report on the observation of fractional quantum numbers at the topological edges and corners in one- and two-dimensional photonic crystals. The fractional quantum numbers are determined via the measurements of the photonic local density-of-states. In one-dimensional photonic crystals, we witness a rapid change of the fractional quantum number at the edges rising from 0 to 1/2 when the photonic band gap experiences a topological transition, confirming the well-known prediction of Jackiw and Rebbi. In two-dimensional systems, we discover that the fractional quantum number in the corner region varies from 0 to 1/2 and 1/4 in different photonic band gap phases. Our study paves a promising way toward topological manipulation of fractional quantum numbers in photonics.