We study magnetic properties of spin glass SG systems under a random field (RF), beased on the suggestion that RFs can be induced by a weak transverse field in the compound LiHo$_x$Y$_{1-x}$F$_4$. We consider a cluster spin model that allows long-range disordered interactions among clusters and short-range interactions inside the clusters, besides a local RF for each spin following a Gaussian distribution with standard deviation $��$. We adopt the one-step replica symmetry breaking (RSB) approach to get an exactly solvable single-cluster problem. We discuss the behavior of order parameters, specific heat $C_{m}$, nonlinear susceptibility $��_3$ and phase diagrams for different disorder configurations. In the absence of RF, the $��_3$ exhibits a divergence at $T_f$, while the $C_{m}$ shows a broad maximum at a temperature $T^{**}$ around 30$\%$ above $T_f$, as expected for conventional SG systems. The presence of RF changes this scenario. The $C_{m}$ still shows the maximum at $T^{**}$ that is weakly dependent on $��$. However, the $T_f$ is displaced to lower temperatures, enhancing considerable the ration $T^{**}/T_f$. Furthermore, the divergence in $��_3$ is replaced by a rounded maximum at a temperature $T^{*}$, which becomes increasingly higher than $T_f$ as $��$ enhances. As a consequence, the paramagnetic phase is unfolded in three regions: (i) a conventional paramagnetism ($T>T^{**}$; (ii) a region with formation of short-range order with frozen spins ($T^{*}

9 pages, 6 figures