  Ly$\alpha$ emission is possibly the best indirect diagnostic of Lyman
continuum (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 this
work, we present the rest UV-optical spectral characteristics of 11 Ly$\alpha$
emitting galaxies at 3 $<$ z $<$ 6 - the optimal redshift range chosen to avoid
the extreme IGM attenuation while simultaneously studying galaxies close enough
to the epoch of reionization. From a combined analysis of JWST/NIRSpec and MUSE
data, we present the Ly$\alpha$ escape fraction and study their correlations
with other physical properties of galaxies that might facilitate Ly$\alpha$
escape. We find that our galaxies have low masses (80\% of the sample with $\rm
log_{10} \ M_{\star} < 9.5\ M_{\odot}$), compact sizes (median $\rm R_e \sim
0.7 \ kpc $), low dust content, moderate [OIII]/[OII] flux ratios (mean $\sim$
6.8 $\pm$ 1.2), and moderate Ly$\alpha$ escape fraction (mean $\rm
f_{esc}^{Ly\alpha} \ \sim$ 0.11). Our sample show characteristics that are
broadly consistent with the low redshift galaxies with Ly$\alpha$ emission,
which are termed as "analogs" of high redshift population. We predict the Lyman
continuum escape fraction in our sample to be low (0.03-0.07), although larger
samples in the post-reionization epoch are needed to confirm these trends.
