The scarcity of superhard materials with magnetism or a narrow band gap, despite their potential applications in various fields, makes it desirable to design such materials. Here, a series of C1+xN1-x compounds are theoretically designed by replacing different numbers of nitrogen atoms with carbon atoms in the synthesized C1N1 compound. The results indicate that the compounds C5N3 and C7N1 possess both superhardness and antiferromagnetic ordering due to the introduction of low-coordinated carbon atoms. The hardness of the two compounds is about 40.3 and 54.5 GPa, respectively. The magnetism in both compounds is attributed to the unpaired electrons in low-coordinated carbon atoms, and the magnetic moments are 0.42 and 0.39 μB, respectively. Interestingly, the magnetism in C5N3 remains unaffected by the external pressure used in this study, whereas C7N1 becomes nonmagnetic when the pressure exceeds ∼80 GPa. Electronic calculations reveal that both compounds behave as indirect band gap semiconductors, with narrow energy gaps of about 0.30 and 0.20 eV, respectively. Additionally, the other two compounds, C6N2-I and C6N2-III, exhibit nonmagnetic ordering and possess hardness values of 52.6 and 35.0 GPa, respectively. C6N2-I behaves as a semiconductor with an energy gap of 0.79 eV, and C6N2-III shows metallic behavior. Notably, the energy gaps of C5N3 and C6N2-I remain nearly constant under arbitrary pressure due to their porous and superhard structure. These compounds fill the gap in magnetic or narrow band gap superhard materials, and they can be used in the spintronic or optoelectronic fields where conventional superhard materials are not suitable.