  We report the first measurements of the $E$ beam-target helicity asymmetry
for the $\vec{\gamma} \vec{n} \to K^{0}\Lambda$, and $K^{0}\Sigma^{0}$ channels
in the energy range 1.70$\leq W\leq$2.34 GeV. The CLAS system at Jefferson Lab
uses a circularly polarized photon beam and a target consisting of
longitudinally polarized solid molecular hydrogen deuteride with low background
contamination for the measurements. The multivariate analysis method boosted
decision trees was used to isolate the reactions of interest. Comparisons with
predictions from the KaonMAID, SAID, and Bonn-Gatchina models are presented.
These results will help separate the isospin $I=0$ and $I=1$ photo-coupling
transition amplitudes in pseudoscalar meson photoproduction.
