  We use the Noether symmetry approach to find $f(R)$ theory of $(2+1)$
dimensional gravity and $(2+1)$ dimensional black hole solution consistent with
this $f(R)$ gravity and the associated symmetry. We obtain $f({R})=D_1
R({n}/{n+1})({R}/{K})^{1/n}+D_2 R+D_3$, where the constant term $D_3$ plays no
dynamical role. Then, we find general spherically symmetric solution for this
$f(R)$ gravity which is potentially capable of being as a black hole. Moreover,
in the special case $D_1=0, D_2={1}$, namely $f(R)=R+D_3$, we obtain a
generalized BTZ black hole which, other than common conserved charges $m$ and
$J$, contains a new conserved charge Q. It is shown that this conserved charge
corresponds to the freedom in the choice of the constant term $D_3$ and
represents symmetry of the action under the transformation $R \rightarrow
R'=R+D_3$ along the killing vector $\partial_{R}$. The ordinary BTZ black hole
is obtained as the special case where $D_3$ is {\it fixed} to be proportional
to the infinitesimal cosmological constant and consequently the symmetry is
broken via Q=0. We study the thermodynamics of the generalized BTZ black hole
and show that its entropy can be described by the Cardy-Verlinde formula.
