To determine which compound requires the least amount of acidified ${KMnO_4}$ for complete oxidation, we need to consider the oxidation states of iron in these compounds and the change in oxidation state during the reaction.
All compounds initially have iron in the +2 oxidation state.
Since all the compounds contain iron in the +2 oxidation state initially, each not requiring any more or less of ${KMnO_4}$ compared to the others based on the moles of iron present in them, what distinguishes them is the presence of other oxidizable ions. Here, ${FeSO_4}$ does not have additional oxidizable components (like in ${FeC_2O_4}$ or ${FeSO_3}$), making it the one requiring the least amount of ${KMnO_4}$.
Therefore, the compound ${FeSO_4}$ requires the least amount of acidified ${KMnO_4}$ for complete oxidation.