Recently, a holey two-dimensional (2D) C₂N crystal with a wide band gap has been successfully synthesized. However, its non-magnetic property largely limits real applications in spintronics. Here we find that edge magnetism can be introduced by tailoring the holey 2D C₂N crystal into nanoribbons with zigzag edges. When edge N atoms are bare or passivated by H atoms, the device can be used to design high-performance thermospin devices and thermal rectifiers. This is ascribed to the emergence of a spin semiconducting property with a wide band gap. Moreover, if the edge N atoms are passivated by O atoms, the device shows a half-metallic property; meanwhile an obvious spin Seebeck effect can also be observed when a temperature difference is applied across the device.