It is a well-known fact that a graph of diameter d has at least $d+1$ eigenvalues. A graph is d-extremal (resp. $d_{\alpha }$-extremal) if it has diameter d and exactly $d+1$ distinct eigenvalues (resp. $\alpha$-eigenvalues), and a graph is split if its vertex set can be partitioned into a clique and a stable set. Such graphs have a diameter of at most three. If all vertex degrees in a split graph are either $\tilde{d}$ or $\widehat{d}$, then we say it is $(\tilde{d},\widehat{d})$-bidegreed. In this paper, we present a complete classification of the connected bidegreed $3_{\alpha }$-extremal split graphs using the association of split graphs with combinatorial designs. This result is a natural generalization of Theorem 4.6 proved by Goldberg et al. and Proposition 3.8 proved by Song et al., respectively.