  We present the first results from an all-sky all-frequency (ASAF) search for
an anisotropic stochastic gravitational-wave background using the data from the
first three observing runs of the Advanced LIGO and Advanced Virgo detectors.
Upper limit maps on broadband anisotropies of a persistent stochastic
background were published for all observing runs of the LIGO-Virgo detectors.
However, a broadband analysis is likely to miss narrowband signals as the
signal-to-noise ratio of a narrowband signal can be significantly reduced when
combined with detector output from other frequencies. Data folding and the
computationally efficient analysis pipeline, {\tt PyStoch}, enable us to
perform the radiometer map-making at every frequency bin. We perform the search
at 3072 {\tt{HEALPix}} equal area pixels uniformly tiling the sky and in every
frequency bin of width $1/32$~Hz in the range $20-1726$~Hz, except for bins
that are likely to contain instrumental artefacts and hence are notched. We do
not find any statistically significant evidence for the existence of narrowband
gravitational-wave signals in the analyzed frequency bins. Therefore, we place
$95\%$ confidence upper limits on the gravitational-wave strain for each
pixel-frequency pair, the limits are in the range $(0.030 - 9.6)
\times10^{-24}$. In addition, we outline a method to identify candidate
pixel-frequency pairs that could be followed up by a more sensitive (and
potentially computationally expensive) search, e.g., a matched-filtering-based
analysis, to look for fainter nearly monochromatic coherent signals. The ASAF
analysis is inherently independent of models describing any spectral or spatial
distribution of power. We demonstrate that the ASAF results can be
appropriately combined over frequencies and sky directions to successfully
recover the broadband directional and isotropic results.
