We here introduce an extension and natural generalization of both the $\kappa$-$\mu$ shadowed and the classical Beckmann fading models: the Fluctuating Beckmann (FB) fading model. This new model considers the clustering of multipath waves on which the line-of-sight (LoS) components randomly fluctuate, together with the effect of in-phase/quadrature power imbalance in the LoS and non-LoS components. Thus, it unifies a variety of important fading distributions as the one-sided Gaussian, Rayleigh, Nakagami- $m$, Rician, $\kappa$ -$\mu$, $\eta$- $\mu$, $\eta$ -$\kappa$, Beckmann, Rician shadowed, and the $\kappa$- $\mu$ shadowed distribution. The chief probability functions of the FB fading model, namely probability density function, cumulative distribution function, and moment generating function are derived. The second-order statistics such as the level crossing rate and the average fade duration are also analyzed. These results can be used to derive some performance metrics of interest of wireless communication systems operating over FB fading channels [ABSTRACT FROM PUBLISHER]