New photometric material is presented for six outer disc supposedly old, Galactic star clusters: Berkeley 76, Haffner 4, Ruprecht 10, Haffner 7, Haffner 11 and Haffner 15, which are projected against the rich and complex Canis Major overdensity at 225{deg}<=l<=248{deg}, -7{deg}b<=-2{deg}. This CCD data set, in the UBVI passbands, is used to derive their fundamental parameters, in particular age and distance. Four of the program clusters turn out to be older than 1Gyr. This fact makes them ideal targets for future spectroscopic campaigns aiming at deriving their metal abundances. This, in turn, contributes to increase the number of well-studied outer disc old open clusters. Only Haffner 15, previously considered an old cluster, is found to be a young, significantly reddened cluster, member of the Perseus arm in the third Galactic quadrant. As for Haffner 4, we suggest an age of about half a Gyr. The most interesting result we found is that Berkeley 76 is probably located at more than 17kpc from the Galactic centre, and therefore is among the most peripherical old open clusters so far detected. Besides, for Ruprecht 10 and Haffner 7, which were never studied before, we propose ages larger than 1Gyr. All the old clusters of this sample are scarcely populated and show evidence of tidal interaction with the Milky Way, and are therefore most probably in advanced stages of dynamical dissolution.