  We consider a metric which describes Ba$\tilde{\text{n}}$ados geometries and
show that the considered metric is a solution of generalized minimal massive
gravity (GMMG) model. We consider the Killing vector field which preserves the
form of considered metric. Using the off-shell quasi-local approach we obtain
the asymptotic conserved charges of given solution. Similar to the Einstein
gravity in the presence of negative cosmological constant, for the GMMG model
also, we show that the algebra among the asymptotic conserved charges is
isomorphic to two copies of the Virasoro algebra. Eventually, we find relation
between the algebra of the near horizon and the asymptotic conserved charges.
This relation show that the main part of the horizon fluffs proposal of
Refs.\cite{140,14} appear for generic black holes in the class of
Ba$\tilde{\text{n}}$ados geometries in the context of GMMG model.
