  Millisecond pulsars (MSPs) are faint X-ray sources commonly observed in
Galactic globular clusters (GCs). In this work, we investigate 18 MSPs newly
found in the GC Omega Centauri ($\omega$ Cen) and search for their X-ray
counterparts using Chandra observations with a total exposure time of 290.9 ks.
We identify confident X-ray counterparts for 11 of the MSPs, with 9 of them
newly identified in this work based on their positions, spectral properties,
and X-ray colours. The X-ray spectra of 9 MSPs are well described by a neutron
star hydrogen atmosphere model, while 2 MSPs are well fitted by a power-law
model. The identified MSPs have X-ray luminosities ranging from
$1.0\times10^{30}$ erg s$^{-1}$ to $1.4\times10^{31}$ erg s$^{-1}$.
Additionally, for population comparison purposes, we study the X-ray
counterpart to MSP E in the GC M71, and find its X-ray spectrum is well
described by blackbody-like models with a luminosity of $1.9\times10^{30}$ erg
s$^{-1}$. We investigate the empirical correlations between X-ray luminosities
and minimum companion masses, as well as mass functions, of spider pulsars.
Clear correlations are observed, with best-fit functions of $\log_{10}{L_X} =
(1.0\pm0.1) \log_{10}{M_{c, min}} + (32.5\pm0.2)$ and $\log_{10}{L_X} =
(0.35\pm0.04) \log_{10}{\rm MF} + (32.71\pm0.20)$, respectively, with an
intrinsic scatter of $\log_{10}{L_X}$ of $\sim$0.3, where $L_X$ is the 0.5$-$10
keV X-ray luminosity, $M_{c, min}$ is the minimum companion mass, and MF
represents the mass function, in solar masses.
