Flat spectrum radio quasars (FSRQs) have been detected at TeV energies by ground-based atmospheric Cherenkov telescope 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 twelve FSRQs, even without detection, provide the first constraints on the duty cycle of TeV emission from these FSRQs. Constraints on the TeV fluxes from these sources are used to probe the origin of the GeV to TeV spectral breaks. From this ongoing survey, the results of the sources observed during 2020-21 season are discussed in this work.