Six new cobalt(II) metal–organic frameworks, {[Co_1.5(TTPA)(BTC)(H₂O)]₂·13H₂O}_n (1), [Co(TTPA)(PA)]_n (2), {[Co(TTPA)(BDA)_0.5(NO₃)]·3H₂O}_n (3), {[Co₂(TTPA)₃(OBA)₂(H₂O)₃]·2CH₃CN·4H₂O}_n (4), {[Co(TTPA)(AIP)(H₂O)]·2H₂O}_n (5), and {[Co(TTPA)(MIP)(H₂O)]·2H₂O}_n (6), have been prepared by the self-assembly of a tris(4-(1H-1,2,4-triazol-1-yl)phenyl)amine (TTPA) ligand with different aromatic carboxylate auxiliary ligands (H₃BTC = 1,3,5-benzenetricarboxylic acid, H₂PA = phthalic acid, H₂BDA = (1,1′-biphenyl)-4,4′-dicarboxylic acid, H₂OBA = 4,4′-oxydibenzoic acid, H₂AIP = 5-aminoisophthalic acid, H₂MIP = 5-methylisophthalic acid) and cobalt salts. Their structures have been characterized by infrared spectroscopy, elemental analysis, single crystal X-ray analysis, and powder X-ray diffraction. Complex 1 is an unusual 4-nodal (3,3,4,8)-connected three-dimensional (3D) new topological net with the point symbol of (4·6·8)₄(4⁴·6⁷·8¹⁵·10²)(6²·8⁴). Complex 2 has a 2-fold interpenetrating 3D dia framework. Complex 3 displays a rare binodal (3,4)-connected 4-fold interpenetrating 3D architecture with a fsc-3,4-C2/c topology with the point symbol of (4·6·8)(4·6²·8³). Complex 4 shows two distinct two-dimensional (2D) layers with hcb topologies, which are further packed into a 3D structure by O–H⋯O hydrogen bonding interactions. Both complexes 5 and 6 feature similar 2D sheets with sql topologies, which can be further packed into a 3D structure by O–H⋯O hydrogen bonding interactions. Moreover, the thermal stability and UV-visible spectra of these complexes are also discussed in detail. Meanwhile, the variable-temperature magnetic susceptibility measurement of complex 1 reveals antiferromagnetic interactions between Co(II) ions.