  We study black hole (BH) solutions in extended Einstein-Maxwell-scalar
theories, which are classified in a subclass of the $U(1)$ gauge-invariant
scalar-vector-tensor theories. The scalar field is coupled to the vector field,
which has electric and magnetic charges. For the static and spherically
symmetric spacetime, we investigate modifications to the Reissner-Nordstr\"{o}m
solutions focusing on the three types of scalar-vector interactions, including
derivative couplings. We solve the field equations analytically in two
asymptotic regions which are the vicinity of the BH horizon and the spatial
infinity, and clarify the condition for the existence of scalar hair. To
understand the behaviors of solutions in intermediate scales, the field
equations are integrated numerically for concrete models with different types
of couplings. We find new hairy BH solutions with scalar hair in the presence
of magnetic charge and kinetic coupling. The magnetic charge plays an important
role in distinguishing hairy BH solutions originated from three types of
different interactions at a large coupling limit.
