One of the primary objectives of the next-generation communication systems is to establish ubiquitous coverage. In this regard, Low Earth Orbit (LEO) satellite networks have attracted significant attention as a promising technology to achieve global coverage. However, fairly and efficiently managing resource allocation, especially beam placement scheduling, poses a significant challenge due to the large number of ground terminals and the vast coverage of LEO satellites. To address this challenge, we model the beam placement scheduling as a problem of minimizing terminal payload at the LEO satellite while considering fairness among terminals. In our proposed solution, we divide the coverage area into segments and use the advantage actor-critic (A2C) to schedule beams within each segment. Our simulations demonstrate that our approach outperforms the greedy method in terms of both throughput and fairness while improving first-time access to the LEO satellite for terminals. Moreover, it outperforms round-robin (RR) scheduling in terms of throughput.