The relativistic quantum motion of scalar bosons under the influence of a full vector (minimal A µ and nonminimal X µ ) and scalar (V s ) interactions embedded in the background of a cosmic string is explored in the context of the Klein-Gordon equation. Considering Coulomb interactions, the effects of this topological defect in equation of motion, phase shift and S-matrix are analyzed and discussed. Bound-state solutions are obtained from poles of the S-matrix and it is shown that bound-state solutions are possible only for a restrict range of coupling constants. PACS. 0 4.62.+v -0 4.20.Jb -0 3.65.Ge -0 3.65.Pm