  We obtain an exact static solution to Einstein-Power-Maxwell (EPM) theory in
$(2+1)$ dimensional AdS spacetime, in which the scalar field couples to gravity
in a non-minimal way. After considering the scalar potential, a stable system
leads to a constraint on the power parameter $k$ of Maxwell field. The solution
contains a curvature singularity at the origin and is non-conformally flat. The
horizon structures are identified, which indicates the physically acceptable
lower bound of mass in according to the existence of black hole solutions.
Especially for the cases with $k>1$, the lower bound is negative, thus there
exist scalar black holes with negative mass. The null geodesics in this
spacetime are also discussed in detail. They are divided into five models,
which are made up of the cases with the following geodesic motions: no-allowed
motion, the circular motion, the elliptic motion and the unbounded spiral
motion.
