The Pdt_xNE alloy system is an established ideal transition-metal system possessing a composition-induced paramagnetic-to-ferromagnetic quantum phase transition (QPT) at the critical concentration xc ~ 0.026 in bulk. A low-temperature non-Fermi liquid (NFL) behavior around xc usually indicates the presence of quantum criticality (QC) in this system. In this work, we explore the existence of such a QPT in nanoparticles of this alloy system. We synthesized single-phase, polydispersed and 40-50 nm mean diameter crystalline nanoparticles of Pdi^N i* alloys, with x near xc and beyond, by a chemical reflux method. In addition to the determination of the size, composition, phase, and crystallinity of the alloys by microscopic and spectroscopic techniques, the existence of a possible QPT was explored by resistivity and dc magnetization measurements. A dip in the value of the exponent n near xc, and a concomitant peak in the constant A of the AT" dependence of the low-temperature (T) resistivity indicate the presence of a quantum-like phase transition in the system. The minimum value of n, however, remains within the Fermi liquid regime (n > 2). The dc magnetization results suggest an anticipatory presence of a superparamagnetic-to-ferromagnetic QPT in the mean-sized nanoparticles. The observation of a possible quantum critical NFL behavior (n < 2) through resistivity is argued to be inhibited by the electron-magnon scatterings present in the smaller nanoparticles.