As the technology node shrinks to the nanometer regime, the demand for new lithography methods with high resolution and low cost is increasing. Electron beam lithography (EBL) is one of the promising next-generation lithography (NGL) technologies that can tackle both challenges compared to the traditional lithography methods. Fogging effect, which causes pattern distortion in layout, is one of the main challenges of widely adopting EBL in technologies below 22nm. This paper proposes a reinforcement-learning (RL) placement method that trains a neural network as an agent to effectively control fogging effect. To speed up our methods compared to two popular placement approaches (i.e., absolute coordinate-based analytical placement and simulated annealing (SA) based placement), we benefit from the following innovations: using topological floorplan representation for our layouts during placement, and deploying an RL trained agent that can intelligently take actions. To more effectively tackle mixed-signal ICs, our method focuses on the sensitive analog devices, which are better protected from potential variations due to fogging effects of other digital/analog portions. The experimental results show that our proposed placer is able to efficiently decrease the fogging effect variation among sensitive transistors in the analog portion up to 92%, while it is 13 and 4.4 times faster than the analytical RL-based placement and SA-based placement methods, respectively.