When the incident solar wind H+ and other minor ions cross a shock, they are decelerated differentially by the electrostatic potential at the shock. Therefore ring beam distributions of the minor ions are formed downstream of a quasi-perpendicular shock in the downstream frame. Moreover, the H+ distribution downstream of the quasi-perpendicular shock usually has large perpendicular temperature anisotropy. The He2+ ring beam distribution and H+ temperature anisotropy can excite helium cyclotron waves and proton cyclotron waves, respectively. In this paper, we perform one-dimensional hybrid simulations to investigate the competition between the helium cyclotron waves and proton cyclotron waves, and their influences on the evolution of He2+ and O6+ velocity distributions are also considered. When the wave spectrum is dominated by the helium cyclotron waves, He2+ and O6+ approximately move on the surface of a sphere, which results in shell-like distributions for He2+and O6+. With the increase of the H+ temperature anisotropy T$perp$p/T$parallel$p, the amplitude of the proton cyclotron waves also increases. When it is sufficiently large and comparable with that of the helium cyclotron waves, the motions of He2+ and O6+ are irregular, which results in bi-Maxwellian distributions of He2+and O6+. We also investigate the influence of the plasma ¿$parallel$p on the excited ion cyclotron waves and the evolution of the He2+and O6+ distributions. The simultaneous observations for He2+ and O6+ in the downstream of shocks with Active Magnetospheric Particle Tracer Explorers (AMPTE)/CCE spacecraft have demonstrated their shell-like distributions. The observed results verify the existence of the helium cyclotron waves downstream of supercritical quasi-perpendicular shocks.