The second generation of stars in the globular clusters (GCs) of the Milky Way (MW) exhibit unusually high N, Na, or Al, compared to typical Galactic halo stars at similar metallicities. The halo field stars enhanced with such elements are believed to have originated in disrupted GCs or escaped from existing GCs. We identify such stars in the metallicity range −3.0 < [Fe/H] < 0.0 from a sample of ∼36,800 giant stars observed in the Sloan Digital Sky Survey and Large Sky Area Multi-Object Fiber Spectroscopic Telescope survey, and present their dynamical properties. The N-rich population (NRP) and N-normal population (NNP) among our giant sample do not exhibit similarities in either in their metallicity distribution function (MDF) or dynamical properties. We find that, even though the MDF of the NRP looks similar to that of the MW’s GCs in the range of [Fe/H] < −1.0, our analysis of the dynamical properties does not indicate similarities between them in the same metallicity range, implying that the escaped members from existing GCs may account for a small fraction of our N-rich stars, or the orbits of the present GCs have been altered by the dynamical friction of the MW. We also find a significant increase in the fraction of N-rich stars in the halo field in the very metal-poor (VMP; [Fe/H] < −2.0) regime, comprising up to ∼20% of the fraction of the N-rich stars below [Fe/H] = −2.5, hinting that partially or fully destroyed VMP GCs may have in some degree contributed to the Galactic halo. A more detailed dynamical analysis of the NRP reveals that our sample of N-rich stars do not share a single common origin. Although a substantial fraction of the N-rich stars seem to originate from the GCs formed in situ, more than 60% of them are not associated with those of typical Galactic populations, but probably have extragalactic origins associated with Gaia Sausage/Enceladus, Sequoia, and Sagittarius dwarf galaxies, as well as with presently unrecognized progenitors.