Understanding continuous phase transitions at zero temperature in strongly correlated electron systems has been one of the intriguing research topics in condensed matter physics. Non-thermal control parameters, such as, chemical disorder, magnetic field, pressure..etc can be used to tune such phase transitions. When quantum fluctuations become sufficiently strong such systems undergo a quantum phase transition (QPT) and heavy fermion metals have emerged as prototypical systems to study quantum critical points (QCP). Recent theories predict a new QCP in disordered itinerant system with exotic properties, such as observable quantum Griffiths phase (QGP). Experiments also indicated that binary Ni-V alloy shows ferromagnetic QPT and leads to QGP through controlled disorder. This observation of QGP in 3d-transition metal system, triggered the research activity in search of new 3d-based alloys to verify the proposed theoretical models. In the present dissertation work, a comprehensive analysis of low-temperature magnetic, electrical transport, and specific heat data of Ni-TM, (TM =V, Cr, Nb) binary and Ni-Cu-Cr ternary alloys has been carried out in the vicinity of critical concentration. From the analysis of magnetic data itineracy was identified using Rhodes-Wohlfarth Ratio. Further from the self-consistent renormalization theory it is shown that spin fluctuations contribution at low temperature can lead to break down of Fermi liquid behavior, which is confirmed from the analysis of low temperature resistivity and specific heat data. These results along with variation of non-universal exponent obtained from magnetic isotherms unequivocally suggest the existence QGP in Ni-Cr and Ni-Cu-Cr alloys, due to presence of strong disorder. Finally, magnetic behavior in Ni-Cr nanoparticles synthesized by novel wire explosion process was investigated and the critical analysis of data suggests a superparamagnetic behavior due to the finite size effects.