  The X-ray emission of neutron stars enables a probe of their temperatures,
geometries, and magnetospheric properties. The current number of X-ray emitting
pulsars is insufficient to rule out observational biases that may arise from
poorly known distance, age, or location of the neutron stars. One approach to
overcome such biases is to create a distance-limited sample with sufficiently
deep observations. With the aim of better sampling of the nearby ($\lesssim$
2kpc) neutron stars population, we started an XMM-Newton survey of pulsars to
measure their X-ray fluxes or derive respective constraining upper limits. We
investigated 14 nearby pulsars for potential X-ray counterparts using different
energy bands and detectors. In addition to our new XMM-Newton data, we also
considered archival data and catalogs. We discuss source properties and also
check for alternative counterparts to the X-ray sources. In our new XMM-Newton
data, we found two pulsar counterpart candidates with significance above over
$4\sigma$ and one candidate with $3.5\sigma$ by combining EPIC camera detection
likelihoods. We also report the detection of potential X-ray counterparts to 8
radio pulsars in the 4XMM-DR10 catalog which have not been reported in the
literature.
