A new Co(II)-based three-dimensional (3D) framework having the molecular formula [Co(C₄O₄)(4-bpmh))H₂O)₂]_n·2nH₂O·2nMeOH·(1)(4-bpmh = N, N-bis-pyridin-4-ylmethylene-hydrazine) has been synthesized using a mixed ligand system and characterized by elemental analysis, IR spectroscopy, thermogravimetric analysis, single crystal X-ray diffraction and variable temperature magnetic study. The framework is constructed by the bridging squarate (C₄O²⁻₄) and N, N-bis-pyridin-4-ylmethylene-hydrazine (4-bpmh) ligands and interpenetration of the 2D grid-like frameworks at definite angles gives rise to 2D$\to$3D inclined polycatenation with sql/Shubnikov tetragonal plane net topology. Extensive non-covalent interactions (H-bonding as well as 𝜋$\cdots$𝜋 interactions) are also observed which stabilises the 3D arrangement. Additionally, complex 1 contains 1D channels of large dimensions (10.91 × 11.78 Ų) that runs along the b-axis. Variable temperature DC magnetic susceptibility study reveals dominant spin–orbit coupling effect typical of the ⁴T_1g ground state of octahedral high-spin Co(II) ion at a higher temperature range.