  To understand the underlying degrees of freedom, near horizon symmetry
analysis of a black has gain significant interest in the recent past. In this
paper we generalized those analysis first by taking into account a generic null
surface carrying $U(1)$ electromagnetic charge. With the appropriate boundary
conditions near the surface under study, we identified the symmetry algebra
among the subset of diffeomporphism and gauge generators which preserve the
metric of the null surface and the form of the gauge field configuration. With
the knowledge of those symmetries we further derived the algebra among the
associated charges considering general Lanczos-Lovelock gravity theory and
gauge theory. Importantly while computing the charges we not only considered
general theory, but also used off-shell formalism which is believed to play
crucial role in understanding quantum gravity. Both the non-extremal and
extremal cases are addressed here.
