  The existence of \emph{weak conical K\"ahler-Einstein} metrics along smooth
hypersurfaces with angle between $0$ and $2\pi$ is obtained by studying a
smooth continuity method and a \emph{local Moser's iteration} technique. In the
case of negative and zero Ricci curvature, the $C^0$ estimate is unobstructed;
while in the case of positive Ricci curvature, the $C^0$ estimate obstructed by
the properness of the \emph{twisted K-Energy}. As soon as the $C^0$ estimate is
achieved, the local Moser iteration could improve the \emph{rough bound} on the
approximations to a \emph{uniform $C^2$ bound}, thus produce a \emph{weak
conical K\"ahler-Einstein} metric. The method used here do not depend on the
bound of any background conical K\"ahler metrics.
