In order to investigate details of the superconducting (SC) gap in the iron-chalcogenide superconductors, the specific heat, C, of FeSe_1-x_Te_x_ with x=0.6-1 has been measured in magnetic fields. Using the two-gap model, it has been found that the smaller SC gap is significantly depressed by the application of magnetic field, resulting in the increase of the slope of the C/T vs T^2^ plot at low temperatures. From the specific-heat measurements at very low temperatures down to 0.4 K, it has been found that the enhancement of the residual electronic-specific-heat-coefficient in the ground state, gamma_0_, by the application of magnetic field is much smaller than that expected for superconductors with the typical s-wave or d-wave SC paring symmetry, which is in sharp contrast to the significant enhancement of gamma_0 observed in the iron-pnictide superconductors. These results are discussed in relation to the multi-band effect in the iron-based superconductors.
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