In this work we use regularized determinant approach to study the discrete spectrum generated by relatively compact non-self-adjoint perturbations of the magnetic Schr\"odinger operator \((-i\nabla - \textbf{\textup{A}})^{2} - b\) in dimension \(3\) with constant magnetic field of strength \(b>0\). The situation near the Landau levels \(2bq\), \(q \in \mathbb{N}\) is more interesting due to the fact that they play the role of thresholds of the spectrum of the free operator. First we obtain sharp upper bounds on the number of complex eigenvalues near the Landau levels. Under appropriate hypothesis we prove the existence of infinite number of complex eigenvalues near each Landau level \(2bq\), \(q \in \mathbb{N}\) and the existence of sectors free of complex eigenvalues. We prove that they are localized in certain sectors adjoining the Landau levels. In particular this answer positively to the problem stays open in [34] of existence of complex eigenvalues accumulating near the Landau levels. Under consideration we prove that the Landau levels are the only possible accumulation point of the complex eigenvalues.