  The baryonic feedback effect is considered as a possible solution to the
so-called $S_8$ tension indicated in cosmic shear cosmology. The baryonic
effect is more significant on smaller scales, and affects the cosmic shear
two-point correlation functions (2PCFs) with different scale- and
redshift-dependencies from those of the cosmological parameters. In this paper,
we use the Hyper Suprime-Cam Year 3 (HSC-Y3) data to measure the cosmic shear
2PCFs ($\xi_{\pm}$) down to 0.28 arcminutes, taking full advantage of the high
number density of source galaxies in the deep HSC data, to explore a possible
signature of the baryonic effect. While the published HSC analysis used the
cosmic shear 2PCFs on angular scales, which are sensitive to the matter power
spectrum at $k\lesssim 1~h{\rm Mpc}^{-1}$, the smaller scale HSC cosmic shear
signal allows us to probe the signature of matter power spectrum up to $k\simeq
20~h{\rm Mpc}^{-1}$. Using the accurate emulator of the nonlinear matter power
spectrum, DarkEmulator2, we show that the dark matter-only model can provide an
acceptable fit to the HSC-Y3 2PCFs down to the smallest scales. In other words,
we do not find any clear signature of the baryonic effects or do not find a
systematic shift in the $S_8$ value with the inclusion of the smaller-scale
information as would be expected if the baryonic effect is significant.
Alternatively, we use a flexible 6-parameter model of the baryonic effects,
which can lead to both enhancement and suppression in the matter power spectrum
compared to the dark matter-only model, to perform the parameter inference of
the HSC-Y3 2PCFs. We find that the small-scale HSC data allow only a fractional
suppression of up to 5 percent in the matter power spectrum at $k\sim 1~h{\rm
Mpc}^{-1}$, which is not sufficient to reconcile the $S_8$ tension.
