The fluctuation-induced conductivity of Ni free and Ni doped Cu0.5Tl0.5Ba2Ca2Cu3−yNiyO10−δ (y=0, 0.5, 1.0, 1.5) samples is investigated for comparison of dimensionality of fluctuations above the mean-field critical temperature. The temperature dependence of paraconductivity can be described by a power law following Aslamazov–Larkin (AL) type equations for these polycrystalline superconductors. It is observed from these studies that at higher temperatures, the fluctuations in the order parameter of the carriers follow two-dimensional (2D) AL behavior, whereas at lower temperatures (closer to transition temperature) their behavior is three-dimensional (3D) AL. From the analysis of our results, we have also evaluated the exponents of dimensionality, the coherence lengths, and the crossover temperatures. The crossover temperature from 2D to 3D have substantially been shifted to lower temperatures with increasing Ni doping, which is most likely related to the scattering of the carriers by remnant spins of Ni atoms. These scattering promote a reduction in the coherence length of the carriers along c-axis. These studies have also shown that the carrier concentration in the conducting CuO2 planes is the most essential; the role of antiferromagnetism in the mechanism of superconductivity is secondary.