The ANTARES neutrino telescope, located in the Mediterranean Sea, and the IceCube neutrino observatory, located at the geographic South Pole, both search for cosmic neutrino events with an instantaneous full-sky field of view. The different characteristics of the two telescopes, in particular the larger instrumented volume of IceCube and the better visibility towards the Southern Sky for neutrino energies below 100 TeV of ANTARES, are exploited in a combined search for point-like and extended sources. The sensitivity to neutrino sources located in the Southern Sky is improved by a factor of $\sim$2 compared to individual studies. The data samples used in this analysis correspond to all track-like and shower-like events from the direction of the Southern Sky which were included in the nine-year ANTARES point-source analysis, combined with the through-going track-like events used in the seven-year IceCube point-source search. In this analysis, the Southern Sky is scanned for possible excesses of neutrinos that might indicate the presence of a source, while the coordinates of predefined candidate neutrinos sources are also evaluated in order to limit the penalty of trials. In addition, special focus is given to the region around the Galactic Centre, treated as an extended neutrinos source, and to the location of the supernova remnant RXJ 1713.7-3946. The result of this combined search for galactic and extra-galactic neutrino sources in the Southern Sky is reported here. No significant evidence of cosmic neutrino sources is found and flux upper limits from the various searches are presented.