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We study a two-dimensional generalized Kemmer oscillator in the cosmic string spacetime with the magnetic field to better understand the contribution from gravitational field caused by topology defects,and present the exact solutions to the generalized Kemmer equation in the cosmic string with the Morse potential and Coulomb-liked potential through using the Nikiforov-Uvarov (NU) method and biconfluent Heun equation method,respectively.Our results give the topological defect’s correction for the wave function,energy spectrum and motion equation,and show that the energy levels of the generalized Kemmer oscillator rely on the angular deficit α connected with the linear mass density m of the cosmic string and characterized the metric’s structure in the cosmic string spacetime.