Nernst effect and torque magnetometry experiments have provided direct evidence for phase-coherence scenario in an iron-based superconductor Fe_1+yTe_1-xSe_x. The Nernst experiment, which measures the transverse electric field when applying a longitudinal temperature gradient and a perpendicular magnetic field, can detect vorticity with high sensitivity. Fe_1+yTe_1-xSe_x with different iron concentration has distinctly different critical temperature T_c, while their vortex-Nernst signal e_N extends to a higher temperature T_onset and remains robust to fields of 13T. The fluctuation diamagnetic signal resolved by high-resolution torque magnetometry also onsets at temperature higher than T_c, and it scales similarly with the vortex-Nernst signal for the same sample. The results support the transition at T_c is caused by the loss of phase-rigidity of Cooper pairs.