Electronic configuration of ${\mathrm{H}}_2^{-}$is ${\left({\sigma }_{1s}\right)}^2,{\left({\sigma }_{1s}^{\ast }\right)}^1$ but not ${\sigma }_{1s}^3,{\sigma }_{1s}^{\ast 0}$ because :

Electronic configuration of ${\mathrm{H}}_2^{-}$is ${\left({\sigma }_{1s}\right)}^2,{\left({\sigma }_{1s}^{\ast }\right)}^1$ but not ${\sigma }_{1s}^3,{\sigma }_{1s}^{\ast 0}$ because, Pauli exclusion principle is violated. According to Pauli's exclusion principle, no two atom's electrons may share the same set of four quantum numbers. This is due to the fact that only two electrons may occupy an orbital, and those two electrons have opposing spins. Pauli's exclusion rule is therefore unbreakable. ${\sigma }_{1s}$ contains 3-electrons out of which 2-electrons must have same spin so, Pauli exclusion rule is violated.