The Ly$alpha$ escape fraction is a key measure to constrain the neutral state of the intergalactic medium and then to understand how the universe was fully reionized. We combine deep narrowband imaging data from the custom-made filter NB393 and the $H_{2}S$1 filter centered at 2.14 $mu$m to examine the Ly$alpha$ emitters and H$alpha$ emitters at the same redshift $z=2.24$. The combination of these two populations allows us to determine the Ly$alpha$ escape fraction at $z=2.24$. Over an area of 383 arcmin$^{2}$ in the Extended Chandra Deep Field South (ECDFS), 124 Ly$alpha$ emitters are detected down to NB393 = 26.4 mag at the 5$sigma$ level, and 56 H$alpha$ emitters come from An14. Of these, four have both Ly$alpha$ and H$alpha$ emissions (LAHAEs). We measure the individual/volumetric Ly$alpha$ escape fraction by comparing the observed Ly$alpha$ luminosity/luminosity density to the extinction-corrected H$alpha$ luminosity/luminosity density. We revisit the extinction correction for H$alpha$ emitters using the Galactic extinction law with the color excess for nebular emission. We also adopt the Calzetti extinction law together with an identical color excess for stellar and nebular regions to explore how the uncertainties in extinction correction affect our results. In both cases, an anti-correlation between the Ly$alpha$ escape fraction and dust attenuation is found among the LAHAEs, suggesting that dust absorption is responsible for the suppression of the escaping Ly$alpha$ photons. However, the estimated Ly$alpha$ escape fraction of individual LAHAEs varies up to ~3 percentage points between the two methods of extinction correction. We find the global Ly$alpha$ escape fraction at $z=2.24$ to be ($3.7pm1.4$)% in the ECDFS. The variation in the color excess of the extinction causes a discrepancy of ~1 percentage point in the global Ly$alpha$ escape fraction.
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