The magnetic structure and the effect of a magnetic field on its domain structure were investigated in a magnetoelectric Y-type hexaferrite, Ba1.3Sr0.7CoZnFe11AlO22, by means of mapping with a micro-focused and circularly polarized X-ray beam in the resonant X-ray diffraction. It was revealed that this hexaferrite exhibits a magnetic order characterized by two distinct antiferromagnetic components: incommensurate helical and commensurate collinear ones, which can be explained as the development of the so-called alternating longitudinal conical structure. A multi-domain state due to the handedness of the helical component, i.e., spin-chirality, is transformed into nearly a mono-domain one by using only a magnetic field. Furthermore, the sign of the spin-chirality in the mono-domain state is reversed by reversing the sign of a magnetic field. These results demonstrate that the spin-chirality in this hexaferrite can be manipulated by a magnetic field alone at room temperature.