  Recently, the modular linear differential equation (MLDE) for level-two
congruence subgroups $\Gamma_\theta, \Gamma^{0}(2)$ and $\Gamma_0(2)$ of
$\text{SL}_2(\mathbb{Z})$ was developed and used to classify the fermionic
rational conformal field theories (RCFT). Two character solutions of the
second-order fermionic MLDE without poles were found and their corresponding
CFTs are identified. Here we extend this analysis to explore the landscape of
three character fermionic RCFTs obtained from the third-order fermionic MLDE
without poles. Especially, we focus on a class of the fermionic RCFTs whose
Neveu-Schwarz sector vacuum character has no free-fermion currents and Ramond
sector saturates the bound $h^{\text{R}} \ge \frac{c}{24}$, which is the
unitarity bound for the supersymmetric case. Most of the solutions can be
mapped to characters of the fermionized WZW models. We find the pairs of
fermionic CFTs whose characters can be combined to produce $K(\tau)$, the
character of the $c=12$ fermionic CFT for $\text{Co}_0$ sporadic group.
