Separating between ordinary (OHE) and anomalous (AHE) Hall effect in the paramagnetic phase of Mn$_{1-x}$Fe$_{x}$Si reveals OHE sign inversion associated with the hidden quantum critical (QC) point $x^*sim0.11$. The semimetallic behavior at intermediate Fe content leads to verifiable predictions in the field of fermiology, magnetic interactions and QC in Mn$_{1-x}$Fe$_{x}$Si. The change of electron and hole concentrations is considered as a driving force for tuning the QC regime in Mn$_{1-x}$Fe$_{x}$Si via modifying of RKKY exchange interaction within the Heisenberg model of magnetism.
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