In order to understand the initial conditions and early evolution of star formation in a wide range of Galactic environments, we carried out an investigation of 64 textit{Planck} Galactic Cold Clumps (PGCCs) in the second quadrant of the Milky Way. Using the $^{13}$CO and C$^{18}$O $J = 1 - 0$ lines, and 850,$mu$m continuum observations, we investigated cloud fragmentation and evolution associated with star formation. We extracted 468 clumps and 117 cores from the $^{13}$CO line and 850,$mu$m continuum maps, respectively. We make use of the Bayesian Distance Calculator and derived the distances of all 64 PGCCs. We found that in general, the mass-size plane follows a relation of $msim r^{1.67}$. At a given scale, the masses of our objects are around 1/10 of that of typical Galactic massive star-forming regions. Analysis of the clump and core masses, virial parameters, densities, and mass-size relation suggests that the PGCCs in our sample have a low core formation efficiency ($sim$3.0%), and most PGCCs are likely low-mass star-forming candidates. Statistical study indicates that the 850,$mu$m cores are more turbulent, more optically thick, and denser than the $^{13}$CO clumps for star formation candidates, suggesting that the 850,$mu$m cores are likely more appropriate future star-formation candidates than the $^{13}$CO clumps.
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