Using JVLA data obtained from high-resolution observations at 5.5 GHz at multiple epochs in 2014 and 2019, we have detected a population of radio variables and transients in the radio bright zone at the Galactic center. With observations covering a sky area of 180 arcmin$^2$ at an angular resolution of 0.4 arcsec, we report new detections of 110 Galactic center compact radio (GCCR) sources with a size of $<1$ arcsec. The flux densities of GCCRs exceed 70 $mu$Jy, with at least 10$sigma$ significance. Among these sources, 82 are variable or transient and 28 are non-variable. About 10% of them are expected to be extragalactic background sources. We discuss the possible astrophysical nature of the detected sources. As compared to the Galactic disk (GD) population of normal pulsars (NPs) and millisecond pulsars (MSPs), a majority (80%) of the GCCRs appears to fall within the high flux-density tail of the pulsar distribution, as extrapolated from a sample of NPs in the Galactic disk. However, MSPs extrapolated from the GD population are too weak to have contributed significantly to the GCCR population that have been detected. We also cross-correlated the GCCRs with X-ray sources in Chandra X-ray catalogs and found that 42 GCCRs have candidate X-ray counterparts. Most of the GCCRs having X-ray counterparts are likely to be associated with unresolved or slightly resolved radio jets launched from X-ray binaries with a compact object, either a black hole or a neutron star.
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