Polycrystalline samples of Cu0.5Tl0.5Ba2Ca2-xNxCu3-yMyO10-δ (M=Ni, Co and Fe N=Mg, Be) superconductor have been synthesized by solid-state reaction method. The structure and physical properties were investigated by powder x-ray diffraction (XRD), scanning electron microscopy (SEM), energy dispersive x-ray analysis (EDX), resistivity, ac-susceptibility and Fourier transforms infrared absorption spectroscopy (FTIR). X-ray diffraction scans of Cu0.5Tl0.5Ba2Ca2Cu3-yMyO10-δ (M = Ni, Co and Fe) samples show tetragonal structure following P4/mmm space group. The dominant phase in these structures is CuTl-1223 with a small inclusion of CuTl-1212 and CuTl-1234 phases. For these samples, there is no remarkable structural transformation (such as tetragonal to orthorhombic) with increased dopant concentration is observed. The system remains tetragonal for the highest critical doping level yc, above which the system is not superconducting. The critical doping levels yc achieved for the dopants are yc=1.5 for M=Ni, yc=0.5 for M=Co and yc=0.075 for M=Fe. The highest critical doping levels are observed for our system, particularly for Ni-doped system. It is observed that the size of the moments bears strong correlation with the critical doping level yc. The Fe-doped system, having a largest localized moment of the order of 5μB, acquires a lowest yc. On the other hand, the Ni-doped system with a smallest moment has a highest yc. Such a correlation represents an observation of interplay between a dopant moment and the suppression of high Tc superconductivity. It strongly suggests a magnetic pair-breaking mechanism. Tc suppression rate is high for Fe- or Co-doped system as compared to Ni- doped system. It is believed that such a large suppression of Tc in Fe- or Co-doped system may originate from oxygen disorder, breaking of Cooper pairs by magnetic impurities (having large magnetic moments) and decrease of carrier concentration in the CuO2 planes. Fe- or Co-doping causes a decrease in carrier concentration through charge transfer which is a consequence of introducing disorder into the CuO2 planes. On the other hand, Ni+2 has the same valence state as Cu+2, Ni substitution for Cu is not expected to effect the carrier concentration. The marginal suppression of Tc in Ni-doped system is may be caused by destruction of anti-ferromagnetism correlation as well as pair breaking effects due to scattering by magnetic impurities. With the partial substitution of Ca with Mg and Be in Ni-doped samples, the CuO2 planes become uniformly doped due to improved inter-planer coupling which results in the enhancement of Tc(R=0) as well as the magnitude of diamagnetism. Superconducting properties of these samples are further enhanced with Li doping at the charge reservoir layer. FTIR absorption measurements show that the phonon modes related to apical oxygen are softened to lower wave number values for Mg- or Be-doped samples confirming that inter-plane coupling have improved in these samples. From the FIC studies of Ni doped samples it is observed that at higher temperature the fluctuations in the order parameter of the carriers follow 2D AL behavior, whereas at lower temperature (closer to transition) their behavior is 3D AL. The cross-over temperature is relatively high in Ni free samples and with Ni doping it is shifted to lower temperature (about 40K). The coherence length calculated from the LD model is decreased with increased Ni doping. The decreased coherence length promotes enhancement of anisotropy of the final compound. Breaking down of anti-ferromagnetic order within the CuO2 planes does not seem to kill the superconductivity; superconductivity and ferromagnetism can co-exist. The effects of carrier concentration on the superconductivity of Cu0.5Tl0.5Ba2Ca2Cu3-yMyO10-δ (M = Ni, Co and Fe) samples are explored by carrying out post-annealing experiments in nitrogen (N2) and oxygen (O2) atmospheres. Superconductivity is suppressed after post-annealing in nitrogen atmosphere. The normal state resistivity of N2-annealed Ni-doped samples is doubled, but its variation with temperature remained metallic down to onset of the superconductivity. The post-annealing in nitrogen atmosphere seems to promote the loss of oxygen from the inter-grain and intra-grain sites; the former increases the ac-losses while the later decreases the magnitude of diamagnetism. On the other hand, the normal state resistivity has decreased after annealing in oxygen atmosphere; resistivity has become one half of the value observed in un-annealed Ni-doped samples. The post-annealing in oxygen has not only improved the inter-grain coupling, but also has remarkably enhanced the magnitude of diamagnetism within the grain. This is most likely accomplished by the oxygen diffusion at the inter-grain sites as well as within the grain.