  One of the primary sources of uncertainties in modeling the cosmic-shear
power spectrum on small scales is the effect of baryonic physics. Accurate
cosmology for Stage-IV surveys requires knowledge of the matter power spectrum
deep in the nonlinear regime at the percent level. Therefore, it is important
to develop reliable mitigation techniques to take into account baryonic
uncertainties if information from small scales is to be considered in the
cosmological analysis. In this work, we develop a new mitigation method for
dealing with baryonic physics for the case of the shear angular power spectrum.
The method is based on an extended covariance matrix that incorporates baryonic
uncertainties informed by hydrodynamical simulations. We use the results from
13 hydrodynamical simulations and the residual errors arising from a fit to a
$\Lambda$CDM model using the extended halo model code {\tt HMCode} to account
for baryonic physics. These residual errors are used to model a so-called
theoretical error covariance matrix that is added to the original covariance
matrix. In order to assess the performance of the method, we use the 2D
tomographic shear from four hydrodynamical simulations that have different
extremes of baryonic parameters as mock data and run a likelihood analysis
comparing the residual bias on $\Omega_m$ and $\sigma_8$ of our method and the
HMCode for an LSST-like survey. We use different modelling of the theoretical
error covariance matrix to test the robustness of the method. We show that it
is possible to reduce the bias in the determination of the tested cosmological
parameters at the price of a modest decrease in the precision.
