Flat spectrum radio quasars (FSRQs) have been detected at TeV energies by ground-based atmospheric Cherenkov telescopes mainly during flaring states. VERITAS is carrying out the first systematic and unbiased search for TeV emissions from a set of FSRQs. Fermi-LAT-detected FSRQs with positive declinations and extrapolated fluxes from the 3FHL catalog exceeding 1$\%$ Crab at >200 GeV after correcting for EBL absorption were selected for this survey, resulting in eight targets. Additionally, four FSRQs that were already detected at TeV energies are also included in this survey. In an unbiased fashion, the observations of 12 FSRQs, even without detection, will provide the first constraints on their duty cycle of TeV emission. We report the results from four of the 12 FSRQs observed during 2020-21 season in this work. For these sources, we also show the results from nearly simultaneous \textit{Fermi}-LAT observations.