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Multistacked GeSiSn/Si quantum dot (MQD) structures of different compositions were obtained by molecular-beam epitaxy. The elastically strained state of GeSiSn/Si MQD structures was confirmed by the presence of diffraction maxima on X-ray rocking curves. The optical properties of GeSiSn/Si MQD structures were studied by Fourier transform infrared (FTIR) photoluminescence spectroscopy. The structures exhibited photoluminescence peaks in the 0.6–0.8 eV range originating from the QD region. The calculations showed that the observed peaks correspond to the radiative transition between the Δ4 conduction band in Si and the energy level of heavy holes in the QDs. The peak positions in the PL spectra are in good correlation with the calculation results. It was demonstrated that the transition energy depends strongly on the composition and size of GeSiSn/Si QDs. The p-i-n photodiodes were developed based on the GeSiSn/Si MQD structures. The cutoff wavelength maximum reached the value of 2.65 μm for Ge0.80Si0.11Sn0.09/Si MQD p-i-n photodiodes.