  We study 10 spectroscopically confirmed Ly$\alpha$ emitters (LAEs) at
$z\approx3.1$ in the UDS field, covered by JWST/NIRCam in the PRIMER program.
All LAEs are detected in all NIRCam bands from F090W to F444W, corresponding to
restframe 2200\AA--1.2$\mathrm{\mu m}$. Based on morphological analysis of the
F200W images, three out of the 10 targets are resolved into pair-like systems
with separations of $<0.9''$, and another three show asymmetric structures. We
then construct the spectral energy distributions (SEDs) of these LAEs. All
sources, including the pairs, show similar SED shapes, with a prominent flux
excess in the F200W band, corresponding to extremely strong [O III]+H$\beta$
emission lines (${\rm EW_{rest}}=740$--$6500\,$\AA). The median effective
radii, stellar mass, and UV slope of our sample are 0.36$\,$kpc,
$3.8\times10^7\,M_\odot$, and --2.48, respectively. The average burst age,
estimated by stellar mass over star formation rate, is $<40\,$Myr. These
measurements reveal an intriguing starbursting dwarf galaxy population lying
off the extrapolations of the $z \sim 3$ scaling relations to the low-mass end:
$\sim 0.7$ dex above the star-forming main sequence, $\sim 0.35$ dex below the
mass--size relation, and bluer in the UV slope than typical high-z galaxies at
similar UV luminosities. We speculate that these numbers may require a larger
main sequence scatter or tail in the dwarf galaxy regime towards the starburst
outliers.
