Based on archival {it Chandra} observations with a total exposure of 1.3 Ms, we study X-ray point sources in the Fornax cluster of galaxies, with the primary aim of searching for intra-cluster X-ray source populations. We detect 1177 point sources out to a projected radius of $sim$30 arcmin ($sim$180 kpc) from the cluster center and down to a limiting 0.5--8 keV luminosity of $sim3times10^{37}{rm~erg~s^{-1}}$. We construct source surface density profile, after excluding sources associated with foreground stars, known globular clusters, ultra-compact dwarfs and galactic nuclei. From this profile we statistically identify $sim$183 excess sources that are not associated with the bulk stellar content of the individual member galaxies of Fornax, nor with the cosmic X-ray background. Taking into account Poisson error and cosmic variance, the cumulative significance of this excess is at $gtrsim 2,sigma$ level (with a maximum of 3.6,$sigma$) outside three effective radii of the central giant elliptical, NGC,1399. The luminosity function of the excess sources is found to be significantly steeper than that of the GC-hosting sources (presumably low-mass X-ray binaries [LMXBs]), disfavoring the possibility that unidentified GCs are primarily responsible for the excess. We show that a large fraction of the excess can be related to the extended stellar halo of NGC,1399 and/or the diffuse intra-cluster light, thus providing strong evidence for the presence of intra-cluster X-ray sources in Fornax, the second unambiguous case for a galaxy cluster after Virgo. Other possible origins of the excess, including supernova-kicked LMXBs and stripped nucleated dwarf galaxies are discussed.
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