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Ly$\alpha$ emission is possibly the best indirect diagnostic of Lymancontinuum (LyC) escape since the conditions that favor the escape of Ly$\alpha$photons are often the same that allows for the escape of LyC photons. In thiswork, we present the rest UV-optical spectral characteristics of 11 Ly$\alpha$emitting galaxies at 3 $<$ z $<$ 6 - the optimal redshift range chosen to avoidthe extreme IGM attenuation while simultaneously studying galaxies close enoughto the epoch of reionization. From a combined analysis of JWST/NIRSpec and MUSEdata, we present the Ly$\alpha$ escape fraction and study their correlationswith other physical properties of galaxies that might facilitate Ly$\alpha$escape. We find that our galaxies have low masses (80\% of the sample with $\rmlog_{10} \ M_{\star} < 9.5\ M_{\odot}$), compact sizes (median $\rm R_e \sim0.7 \ kpc $), low dust content, moderate [OIII]/[OII] flux ratios (mean $\sim$6.8 $\pm$ 1.2), and moderate Ly$\alpha$ escape fraction (mean $\rmf_{esc}^{Ly\alpha} \ \sim$ 0.11). Our sample show characteristics that arebroadly consistent with the low redshift galaxies with Ly$\alpha$ emission,which are termed as "analogs" of high redshift population. We predict the Lymancontinuum escape fraction in our sample to be low (0.03-0.07), although largersamples in the post-reionization epoch are needed to confirm these trends.

Early Results from GLASS-JWST XXII: Rest frame UV-optical spectral properties of Lyman-alpha emitting galaxies at 3 $<$ z $<$ 6