  It is widely accepted that X-ray emission in luminous active galactic nuclei
(AGNs) originates from hot corona. To prevent the corona from over-cooling by
strong X-ray emission, steady heating to the corona is essential, for which the
most promising mechanisms is the magnetic reconnection. Detailed studies of the
coupled disc and corona, in the frame of magnetic field transferring
accretion-released energy from the disc to the corona, reveal that the thermal
electrons can only produce X-ray spectrum with $\Gamma_{\rm 2-10\,keV}>2.1$,
which is an inevitable consequence of the radiative coupling of the thermal
corona and disc. In the present work, we develop the
magnetic-reconnection-heated corona model by taking into account the potential
non-thermal electrons accelerated in the magnetic reconnection process, in
addition to the thermal electrons. We show that the features of the structure
and spectrum of the coupled disc and corona can be affected by the fraction of
magnetic energy allocated to thermal electrons. Furthermore, we investigate the
effects of the power-law index and energy range of non-thermal electrons and
the magnetic field on the spectrum. It is found that the X-ray spectrum from
the Comptonization of the hybrid electrons can be flatter than that from
thermal electrons only, in agreement with observations. By comparing with the
observed hard X-ray data, we suggest that a large fraction ($>40\%$) of the
magnetic energy be allocated to the non-thermal electrons in the luminous and
flat X-ray spectrum AGNs.
