The borax bead test gives characteristic colours only for transition-metal ions with partially filled $d$-orbitals. Zn${}^{2+}$ ($d^{10}$) does not give a coloured bead, so it is excluded.

Among Fe${}^{2+}$, Fe${}^{3+}$ and Cr${}^{2+}$, all are coloured and give positive borax bead tests. The relevant ionisation comparison is the energy needed to form each cation from its element. Formation of Fe${}^{3+}$ requires removing three electrons (sum of first three IEs), which exceeds the energy required to form the divalent Fe${}^{2+}$ or Cr${}^{2+}$.

Hence Fe${}^{3+}$ both shows a positive borax bead test (yellow-brown) and has the highest cumulative ionisation enthalpy.