  We generalize our previous studies on the Maxwell quasinormal modes around
Schwarzschild-anti-de-Sitter black holes with Robin type vanishing energy flux
boundary conditions, by adding a global monopole on the background. We first
formulate the Maxwell equations both in the Regge-Wheeler-Zerilli and in the
Teukolsky formalisms and derive, based on the vanishing energy flux principle,
two boundary conditions in each formalism. The Maxwell equations are then
solved analytically in pure anti-de Sitter spacetimes with a global monopole,
and two different normal modes are obtained due to the existence of the
monopole parameter. In the small black hole and low frequency approximations,
the Maxwell quasinormal modes are solved perturbatively on top of normal modes
by using an asymptotic matching method, while beyond the aforementioned
approximation, the Maxwell quasinormal modes are obtained numerically. We
analyze the Maxwell quasinormal spectrum by varying the angular momentum
quantum number $\ell$, the overtone number $N$, and in particular, the monopole
parameter $8\pi\eta^2$. We show explicitly, through calculating quasinormal
frequencies with both boundary conditions, that the global monopole produces
the repulsive force.
