Key concept Molecules or ions having odd number of electrons are paramagnetic in nature.
$O_2^+$ ion electronic configuration:
$\sigma1s^{2}, \sigma^{ ? },1s^{2},\sigma^{ ? }2s^{2},\sigma2p_{z^{^2}},$
$\quad\quad\quad\quad\quad\quad\begin{Bmatrix}\pi2p_{x^{2}}\\ \pi2p_{y^{2}}\end{Bmatrix}\begin{Bmatrix}?\quad\quad\\ \pi2p_{x^{1}}\\ ?\quad\quad\\ \pi2p_{y}\end{Bmatrix}\begin{matrix}?\quad\quad\\ \sigma2p_{z}\end{matrix}$
Total number of electrons 16 - 1 = 15
It is paramagnetic
Bond order = $\frac{10-5}{2} = 25$ (more stable)
$O_{2}^{-}$ ion electronic configuration
$\sigma1s^{2},^{ ? }\sigma1s^{2},\sigma2s^{2},^{ ? }\sigma2s^{2},\sigma2p^{2}_{z},$
$\quad\quad\quad\quad\quad\quad\begin{Bmatrix}\pi2p_{x^{2}}\\ \pi2p_{y^{2}}\end{Bmatrix}\begin{Bmatrix}?\quad\quad\\ \pi2p_{x^{1}}\\ ?\quad\quad\\ \pi2p_{y}\end{Bmatrix}\begin{matrix}?\quad\quad\\ \sigma2p_{z}\end{matrix}$
Total number of electrons = 16 + 1 = 17
It is paramagnetic.
Bond order = $\frac{10-7}{7}=\frac{3}{2} = 1.5$ (less stable)