Spectral Turán problem for ${\mathcal{K}}_{2,t}^{-}$-free unbalanced signed graphs

We determine the maximum index and the signed graphs with the maximum index among all ${\mathcal{K}}_{2,t}^{-}$-free unbalanced signed graphs with fixed order for $t\ge 3$, as well as the second maximum index and the signed graphs with the second maximum index among all ${\mathcal{K}}_{2,t}^{-}$-free unbalanced signed graphs with fixed order for $t\ge 4$.