We report the discovery of a $z_{phot}=6.18^{+0.05}_{-0.07}$ (95% confidence level) dwarf galaxy, lensed into four images by the galaxy cluster MACS J0329.6-0211 ($z_{l}=0.45$). The galaxy is observed as a high-redshift dropout in \emph{HST}/ACS/WFC3 CLASH and \emph{Spitzer}/IRAC imaging. Its redshift is securely determined due to a clear detection of the Lyman-break in the 18-band photometry, making this galaxy one of the highest-redshift multiply-lensed objects known to date with an observed magnitude of F125W$=24.00\pm0.04$ AB $mag$ for its highest-magnified image. We also present the first strong-lensing analysis of this cluster uncovering 15 additional multiply-imaged candidates of five lower-redshift sources spanning the range $z_{s}\simeq2-4$. The mass model independently supports the high photometric redshift and reveals magnifications of $11.6^{+8.9}_{-4.1}$, $17.6^{+6.2}_{-3.9}$, $3.9^{+3.0}_{-1.7}$, and $3.7^{+1.3}_{-0.2}$, respectively, for the four images of the high-redshift galaxy. With this we construct a source image with a physical resolution of $\sim200$ pc when the universe was $\sim0.9$ Gyr old, where the $z\simeq6.2$ galaxy occupies a source-plane area of approximately 2.2 kpc$^{2}$. Modeling the observed spectral energy distribution using population synthesis models, we find a demagnified stellar mass of $\sim10^{9} \mathcal{M}_{\sun}$, subsolar metallicity ($Z/Z_{\sun}\sim0.5$), low dust content ($A_{V}\sim0.1$ mag), a demagnified star formation rate (SFR) of $\sim3.2 \mathcal{M}_{\sun}$ yr$^{-1}$, and a specific SFR of $\sim3.4$ Gyr$^{-1}$, all consistent with the properties of local dwarf galaxies.

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