We have experimentally investigated the fluxon dynamics in a narrow ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}\mathrm{Ca}{\mathrm{Cu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ stack with junction length $L\ensuremath{\sim}1.8\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$. As an evidence of high-frequency excitation by a collective cavity mode, under an (in-plane) external magnetic field, the current-voltage characteristics show prominent Fiske steps with the corresponding resonance frequencies of $75--305\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$. Further study of flux-flow resistance oscillation with various $c$-axis currents clarifies the correlation with Fiske steps by distinguishing two different regions, i.e., the static flux-flow region at low bias current level and dynamic Fiske step region at high bias current level.