Sorry if this sounds a bit vague, I don't know Calis very well. Nearly 3 weeks ago I rescued a black kitten - all skin and bone, from a pile of builder's rubble in the yard of an apartment block occupied it seemed by Turks. Our friends who have now returned to the UK, had been feeding a number of kittens up there. She knew I wanted a black kitten (long story) and we went up to have a look. It was nearly three weeks ago on a day when it poured down all day. There were quite a few kittens there of all ages with no adult cats in sight. They were being "fed" with the usual scraps and left overs.
When we saw our friends a couple of weeks ago we mentioned the kittens and asked how they were. They said they were ok but that there seemed to be even more appearing there. We went up to look again and they all seemed ok apart from one tiny kitten who was too small to eat the food put out. I decided "in for a penny, in for a pound" and took it. It's predominantly white with a few coloured blotches so definitely not yours! Whilst we were holding her a couple of little Turkish girls came along (I think they'd got off a school bus). At first the one tried to take the kitten from me and I asked her if it was hers. She didn't answer and I asked where she lived and if her mum was at home. She suddenly pushed the kitten back to me and ran away.
It may be nothing, it may be a couple of little girls collecting kittens to feed and play with. If you see the girls can you follow them home? I imagine the one was about 9 or 10, but wouldn't swear to it. She had shoulder length hair and I seem to remember her wearing rather a lot of pink and carrying a pink rucksack.
I can't describe where the apartment block was other than in general terms - our friends live right by the bowling club on up past the Ambar restaurant and the apartments were a distance beyond them, walking away from the coast. If you think this might be a possibility I can try and contact our friends and get more specific directions. If you can spot your kitten and ownership comes into debate suggest that your kitten has been microchipped. I found mention of Jandarma put the wind up a neighbour's son sufficiently last week to induce quite a few tears and the return of our property!
Good luck, and if I can help let me know.