  In this work, we calculated the sizes of unresolved X-ray emission regions in
three gravitationally lensed radio-loud quasars, B\,1422+231, MG\,J0414+0534
and Q\,0957+561, using a combination of imaging and spectral analysis on the
X-ray data taken from the \textit{Chandra X-Ray Observatory}. We tentatively
detected FeK$\alpha$ emission lines in MG\,J0414+0534 and Q\,0957+561 with over
95\% significance, whereas, we did not significantly detect FeK$\alpha$
emission in B\,1422+231. We constructed differential microlensing light curves
from absorption corrected count rates. We subsequently performed a microlensing
analysis on the X-ray microlensing light curves to measure the X-ray source
sizes in soft (0.83--3.6 keV), hard (3.6--21.8 keV), and full (0.83--21.8 keV)
bands, based on either Bayesian or maximum likelihood probabilities. For
B\,1422+231, sizes from the two methods are consistent with each other, e.g.
$R_X^{hard}/R_G = 6.17\pm5.48 \text{ (Bayesian), } 11.81\pm3.75 \text{ (maximum
likelihood)}$, where $R_G=GM_{BH}/c^2)$. However, for MG\,J0414+0534 and
Q\,0957+561, the two methods yield completely different results suggesting that
more frequently sampled data with better signal-to-noise ratio are needed to
measure the source size for these two objects. Comparing the acquired size
values with the radio-quiet sample in the literature we found that our results
are consistent with X-ray source size scaling approximately as $R_X \propto
M_{BH}$ with the mass of the central supermassive black hole. Our results also
indicate that radio-loud quasars tend to have larger unresolved X-ray emission
sizes compared to the radio-quiet ones.
