When the coordination sites of ligands were shifted, the solvothermal reactions of four positional isomeric asymmetrical pyridyldicarboxylatic acids with Cd(NO3)2 generated four new coordination polymers, [Cd(L1)(DMF)3]·DMF·H2O (1), [H2N(CH3)2]2[Cd(L2)2]·3DMF·H2O (2), [Cd(L3)(H2O)2] (3), and [Cd(L4)]·1.5DMF (4), where DMF = N,N-dimethylformamide, H2L1 = 2-(3'-carboxylphenyl)isonicotinic acid, H2L2 = 2-(4'-carboxylphenyl)isonicotinic acid, H2L3 = 5-(3'-carboxylphenyl)nicotic acid, and H2L4 = 2-(3'-pyridyl)terephthalic acid. 1 shows a rare 2D fabric structure. 2 discloses a grid-layer structure with heterochiral helical chains and in which three sets of layers stack in different directions, affording an unprecedented 2D + 2D + 2D → 3D polycatenating framework with 3D intersecting porous systems. 3 also displays a 2D layer possessing strong intralayer π···π interactions and interlayer hydrogen bonds. 4 contains a rare Cd2(COO)4 paddle-wheel unit and forms a 3D framework with 1D open channels. The carboxyl and pyridyl groups of the positional isomeric H2L1-H2L4 ligands show distinct bridging fashions, which leads to the production of versatile architectures of 1-4, and their effects on the crystal structures are discussed. 1-4 reveal solid-state photoluminescence stemming from intraligand charge transfer. 2 and 4 show high selectivity for CO2 over CH4 but with different CO2 adsorption enthalpies. Grand canonical Monte Carlo simulations identified the multiple adsorption sites in 2 for CO2.