The metal ion whose electronic configuration is not affected by the nature of the ligand and which gives a violet colour in non-luminous flame under hot condition in borax bead test is

Ni⁺² gives violet colored bead in non-luminous flame under hot conditions. Ni⁺² has d⁸ configuration which does not depend on the nature of ligand present in octahedral complex.
${\mathrm{Ni}}^{+2} : {{\mathrm{t}}_{2\mathrm{g}}}^6{{\mathrm{e}}_{\mathrm{g}}}^2$