A novel quaternary compound in the Ba-Y-Fe-O phase diagram was synthesized by solid-state reaction and its crystal structure was characterized using powder X-ray diffraction. The crystal structure of BaYFeO4 consists of a unique arrangement of Fe3+ magnetic ions, which is based on alternate corner-shared units of [FeO5](7-) square pyramids and [FeO6](9-) octahedra. This results in the formation of stairwise channels of FeO polyhedra along the b crystallographic axis. The structure is described in an orthorhombic crystal system in the space group Pnma with lattice parameters a = 13.14455(1) angstrom, b = 5.694960(5) angstrom, and c = 10.247630(9) angstrom. The temperature-dependent magnetic susceptibility data reveal two antiferromagnetic (AFM) transitions at 33 and 48 K. An upturn in the magnetic susceptibility data above these transitions is observed, which does not reach its maximum even at 390 K. The field-dependent magnetization data at both 2 and 300 K show a nearly linear dependence and do not exhibit significant hysteresis. Heat capacity measurements between 2 and 200 K reveal only a broad anomaly without any indication of long-range ordering. The latter data set is not in good agreement with the magnetic susceptibility data, which makes it difficult to exactly determine the magnetic ground state of BaYFeO4. Accordingly, a temperature-dependent neutron diffraction study is in order, which will enable resolving this issue. The theoretical study of the relative strengths of magnetic exchange interactions along various possible pathways, using extended Huckel spin dimer analysis, shows that only interactions between square pyramidal and octahedral centers are significant, and among them, the intrachannel correlations are stronger than interchannel interactions. This is the first physical property study in such a magnetic ion substructure.