For the in-memory computation architecture, a ferroelectric semiconductor field-effect transistor (FeSFET) incorporates ferroelectric material into the FET channel to realize logic and memory in a single device. The emerging group III nitride material Al1−xScxN provides an excellent platform to explore FeSFET, as this material has significant electric polarization, ferroelectric switching, and high carrier mobility. However, steps need to be taken to reduce the large band gap of ∼5 eV of Al1−xScxN to improve its transport property for in-memory logic applications. By state-of-the-art first principles analysis, here we predict that alloying a relatively small amount (less than ∼5%) of Sb impurities into Al1−xScxN very effectively reduces the band gap while maintaining excellent ferroelectricity. We show that the co-doped Sb and Sc act cooperatively to give a significant band bowing leading to a small band gap of ∼1.76 eV and a large polarization parameter ∼0.87 C/m2, in the quaternary Al1−xScxSbyN1−y compounds. The Sb impurity states become more continuous as a result of interactions with Sc and can be used for impurity-mediated transport. Based on the Landau-Khalatnikov model, the Landau parameters and the corresponding ferroelectric hysteresis loops are obtained for the quaternary compounds. These findings indicate that Al1−xScxSbyN1−y is an excellent candidate as the channel material of FeSFET.