The modified two-stream instability in the foot of supercritical quasi-perpendicular shock wave is investigated. A linear analysis shows that the instability can sufficiently grow during the shock reformation cycle for the case of a realistic ion to electron mass ratio. The wave-particle interactions of the Landau type of both the electrons and ions are essential in a finite beta plasma and lead to a reduction of the growth rate with increasing beta. The magnetic polarization in terms of wavevector is also analyzed. Additional one-dimensional full-particle electromagnetic simulations in a periodic system reveal some important nonlinear wave properties. The wave spectra indicate a lower cascade due to wave-wave interactions. The parallel phase space distribution of electrons correlates well with the wave profile of the magnetic field component perpendicular to both the ambient magnetic field and the wavevector. The nonlinearly generated waves lead to electron heating parallel to the magnetic field.