The detection of variable stars in open clusters is an essential component of testing stellar structure and evolution theories. The ability to detect low-amplitude variability among cluster members is directly related to the quality of the photometric results. Point Spread Function (PSF) fitting is the best method available for measuring accurate magnitudes within crowded fields of stars, while high-precision differential photometry is the preferred technique for removing the effects of atmospheric extinction and variable seeing. In the search for new variable stars among hundreds or thousands of stars, the Robust Median Statistic (RoMS) is proven more effective for finding low-amplitude variables than the traditional error curve approach. A reputable computer program called DAOPHOT was used to perform PSF fitting, whereas programs, CLUSTER and RoMS, were created to carry out high-precision differential photometry and calculate the RoMS, respectively, on the open clusters NGC 225, NGC 559, NGC 6811, NGC 6940, NGC 7142, and NGC 7160. Twenty-two new variables and eighty-seven suspected variable stars were discovered, and time-series data of the new variables are presented.