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Abstract Dual and off-nucleus active supermassive black holes are expected to be common in the hierarchical structure formation paradigm, but their identification at parsec scales remains a challenge due to strict angular resolution requirements. We conducted a systematic study using the Very Long Baseline Array (VLBA) to examine 23 radio-bright candidate dual and off-nucleus quasars. The targets are selected by a novel astrometric technique (varstrometry) from Gaia, aiming to identify dual or off-nucleus quasars at (sub)kiloparsec scales. Among these quasars, eight exhibit either multiple radio components or significant (>3σ) positional offsets between the VLBA and Gaia positions. The radio emission from the three candidates, which exhibit multiple radio components, is likely to originate from small-scale jets based on their morphology. Among the remaining five candidates with significant VLBA-Gaia offsets, three are identified as potential dual quasars at parsec scales, one is likely attributed to small-scale jets, and the origin of the last candidate remains unclear. We explore alternative explanations for the observed VLBA-Gaia offsets. We find no evidence for optical jets at kiloparsec scales, nor any contamination to Gaia astrometric noise from the host galaxy; misaligned coordinate systems are unlikely to account for our offsets. Our study highlights the promise of the varstrometry technique in discovering candidate dual or off-nucleus quasars and emphasizes the need for further confirmation and investigation to validate and understand these intriguing candidates.