Two three-dimensional (3D) coordination networks, [Co₃(1,4-BDC)3(L¹)]_∞ (L¹ = N,N′-bis(3-pyridinyl)-1,4-benzenedicarboxamide; 1,4-H₂BDC = 1,4-benzenedicarboxylic acid), 1, and [K₂Co₃(L²)₄]_∞ (H₂L² = 5-acetamidoisophthalic acid), 2, have been synthesized by hydrothermal reactions and characterized by single crystal X-ray crystallography. Complex 1 consists of linear trinuclear Co(II) centers, which are linked by the 1,4-BDC⁻ and L¹ ligands to form a rare (1 + 3) self-catenated 3D net with the new (3⁶,4¹⁰,5¹¹,6) topology, and complex 2 reveals a 3p–3d heterometallic coordination network based on linear trinuclear Co(II) and dinuclear K(I) centers bridged by the μ₆-L² ligands, forming a 4,4,8-connected trinodal net with the new (4¹⁴·6¹⁰·8⁴)(4²·6⁴)(4⁴·6²) topology. The linear trinuclear Co(II) centers in 1 adopt the square pyramidal–octahedral–square pyramidal geometries, whereas those in 2 are tetrahedral–octahedral–tetrahedral. Both of the complexes exhibit paramagnetism that is consistent with the Curie–Weiss law between 60 and 300 K. The effective magnetic moments (〈μ_eff〉) of both complexes are larger than the estimated value of 6.71 μ_B/f.u., revealing the spin–orbit couplings that are invoked by the different distorted geometries of the linear trinuclear Co(II) centers. The dinuclear K(I) centers in 2 weaken the magnetic coupling, and reduce the antiferromagnetic ordering at 6 K.