In this work, we report new quasars discovered in fields in the vicinity of the Andromeda (M31) and Triangulum (M33) galaxies with the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST, also called the Guo Shou Jing Telescope) during the 2013 observational season, the second year of the regular survey. In total, 1330 new quasars are discovered in an area of ~133{deg}^2^ around M31 and M33. With i magnitudes ranging from 14.79 to 20.0 and redshifts from 0.08 to 4.85, the 1330 new quasars represent a significant increase in the number of identified quasars in fields in the vicinity of M31 and M33. Up to now, there have been a total of 1870 quasars discovered by LAMOST in this area. The much enlarged sample of known quasars in this area can potentially be utilized to construct a precise astrometric reference frame for the measurement of minute proper motions of M31, M33 and their associated substructures, which are vital for understanding the formation and evolution of M31, M33 and the Local Group of galaxies. Moreover, in the sample, there are a total of 45, 98 and 225 quasars with i magnitudes brighter than 17.0, 17.5 and 18.0 respectively. In the aforementioned brightness bins, 15, 35 and 84 quasars are reported here for the first time, and 6, 21 and 81 are reported in our previous work. In addition, 0, 1 and 6 are from the Sloan Digital Sky Survey and 24, 41 and 54 are from the NED database. These bright quasars provide an invaluable sample to study the kinematics and chemistry of the interstellar/intergalactic medium of the Local Group.

Cone search capability for table J/other/RAA/15.1438/table1 (Catalog of new quasars in fields in the vicinity of M31 and M33 discovered by LAMOST in the 2013 observational season)