The generalized form of Killingbeck potential is an attractive Coulomb term plus a linear term and a harmonic oscillator term, i.e. −a/r + br + λr ², which has a useful application in quarkonium spectroscopy. The ground state energy with the corresponding wave function are obtained for any arbitrary m-state in two-dimensional Klein–Gordon equation with equal mixture of scalar–vector Killingbeck potentials in the presence of constant magnetic and singular Ahoronov–Bohm flux fields perpendicular to the plane where the interacting charged particle is confined. The analytical exact iteration method is used in our solution. We obtain the energy eigensolutions for particle and antiparticle corresponding to S(r) = V(r) and S(r) = −V(r) cases, respectively. Some special cases like the Coulomb, harmonic oscillator potentials and the nonrelativistic limits are found in presence and absence of external fields.