Recent observations demonstrated that emerging flux regions, which constitute the early stage of solar active regions, consist of emergence of numerous small-scale magnetic elements. They in turn interact, merge, and form mature sunspots. However, observations of fine magnetic structures on photosphere with sub-arcsecond resolution are very rare due to limitations of observing facilities. In this work, taking advantage of the high resolution of the 1.6 m Goode Solar Telescope, we jointly analyze vector magnetic fields, continuum images, and H{alpha} observations of NOAA AR 12665 on 2017 July 13, with the goal of understanding the signatures of small-scale flux emergence, as well as their atmospheric responses as they emerge through multiple heights in photosphere and chromosphere. Under such a high resolution of 0.1 to 0.2, our results confirm two kinds of small-scale flux emergence: magnetic flux sheet emergence associated with the newly forming granules, and the traditional magnetic flux loop emergence. With direct imaging in the broadband TiO, we observe that both types of flux emergence are associated with darkening of granular boundaries, while only flux sheets elongate granules along the direction of emerging magnetic fields and expand laterally. With a life span of 10--15 minutes, the total emerged vertical flux is in order of 10$^{18}$ Mx for both types of emergence. The magnitudes of the vertical and horizontal fields are comparable in the flux sheets, while the former is stronger in flux loops. H{alpha} observations reveal transient brightenings in the wings in the events of magnetic loop emergence, which are most probably the signatures of Ellerman bombs.
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