By employing Y-shaped N-heterocyclic carboxylic acid 4,4′-(1H-1,2,4-triazol-1-yl)methylene-bis(benzoic acid) (H₂TZMB) and pyridine ancillary linkers (4,4′-bipy = 4,4′-bipyridine, 1,4-bipb = 1,4-bis(pyrid-4-yl)benzene and 4,4′-bipb = 4,4′-bis(pyrid-4-yl)biphenyl), five new coordination polymers (CPs), namely, {[Cd(TZMB)(DMA)]·(H₂O)_0.5}_n (1), {[Cd(HTZMB)₂(4,4′-bipb)]·(4,4′-bipb)(H₂O)_0.5}_n (2), {[Ni(TZMB)(1,4-bipb)(H₂O)]·H₂O}_n (3),{[Ni(TZMB)(4,4′-bipy)(H₂O)_1.5]·(H₂O)_3.5}_n (4) and {[Mn₂(TZMB)₂(H₂O)(DMA)]·DMA}_n (5), have been obtained and characterized. Structural analyses reveal that 1 is a 2D (3,6)-connected {4³}₂{4⁶·6⁶·8³} net based on binuclear {Cd₂(COO)₄} SBUs. The 2D structure of 2 exhibits a uninodal 4-connected net with the point symbol of {4⁴·6²}. 3 shows a 3D (3,5)-connected net with the point symbol of {4·6·8}{4·6⁴·8⁵}. 4 presents a 3D (4,6)-connected net based on binuclear {Ni₂(COO)₂(μ₂-H₂O)} SBUs with the point symbol of {3·4·5³·6}{3²·4²·5⁵·6⁵·7}. 5 indicates a 3D 3-nodal (3,4,7)-connected net with 1D rod-like {Mn₂(COO)₄}_n SBUs with the point symbol of {4²·6}{4⁴·6²}{4⁶·6⁹·8⁶}. Luminescence properties of 1 and 2 demonstrate that they have potential applications in luminescence sensing for NACs and Fe³⁺ ions, and then luminescence quenching mechanisms were systematically investigated. Furthermore, magnetic measurements of 3–5 indicate that there exist ferromagnetic interactions between adjacent Ni(II) ions in 3 and 4 and antiferromagnetic interaction between adjacent Mn(II) ions in 5.