Bound states in the continuum (BICs) are general discrete mode points that typically have narrow-angle responses. To break this limitation on the performance of BICs, we propose a magneto-optical photonic crystal slab and study its eigen modes and far-field polarizations. Unlike general BICs, we find a continuous distribution with a ring shape for the quasi-BICs in k-space and analyze the forming mechanism. The ring BICs provide a special response of spatial directions and can be modulated by multiple structural parameters. Different from the linear polarizations of far-field from general BICs, the far-field polarizations within the ring qBICs are either ideally circular polarization or elliptical polarizations with all potential values of ellipticities leading to infinite density of states. The ring qBICs allow us to manipulate the polarization with more degrees of freedom for potential applications.