  We present a detailed spectral-timing analysis of the Kilohertz
quasi-periodic oscillations (kHz QPOs) in Sco X-1 using the data of Rossi X-ray
Timing Explorer ($RXTE$) and the Hard X-ray Modulation Telescope
($Insight$-HXMT). The energy band with detectable kHz QPOs is studied for the
first time: on the horizontal branch, it is $\sim$ 6.89--24.01 keV and $\sim$
8.68--21.78 keV for the upper and lower kHz QPOs detected by $RXTE$, and $\sim$
9--27.5 keV for the upper kHz QPOs by $Insight$-HXMT; on the lower normal
branch, the energy band is narrower. The fractional root mean square (rms) of
the kHz QPOs increases with energy at lower energy, reaches a plateau at about
16 keV and 20 keV for the lower and upper peaks, and then levels off though
with a large uncertainty. The simulation of the deadtime effect of $RXTE$/PCA
shows that the deadtime does not affect much the search of the kHz QPOs but
makes the rms amplitude underestimated. No significant QPO is detected below
$\sim$ 6 keV as shown by the $RXTE$ data, implying that the kHz QPOs do not
originate from the black body emission of the accretion disk and neutron star
surface. In addition, with the combined analysis of the energy spectra and the
absolute rms spectra of kHz QPOs, we suggest that the kHz QPOs in Sco X-1
originate from the Comptonization of the inner part of the transition layer,
where the rotation sets the frequency and the inward bulk motion makes the
spectrum harder.
