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Polycrystalline samples Co₃Sn₂S_2+x (0 ≤ x ≤ 0.34) and (Co_1-xM_x)₃Sn₂S_2.26 (M = Ni and Fe, 0 ≤ x ≤ 0.05) have been synthesized using solid-state-reaction and characterized by X-ray diffraction (XRD) and electron probe microanalyzer (EPMA). Basically, we are able to reproduce the phase diagram (so-called A phase) as previously reported with negligible sample dependent effect. Furthermore, following the similar procedure and analysis, a so-called A' phase within phase can be sketched in H-T phase diagram of Co₃Sn₂S₂. Under the effects of external high-pressure and chemical substitutions, the anomalous magnetisms (A and A' ) in low magnetic field show a significant change. The possible origin of the field-induced A' phase could be ascribed to the non-collinear skyrmion-like phenomena. These striking findings provide a new candidate in spin-frustrated systems to explore the complexity of magnetic-field-induced magnetism.