Dfyjkt

I am travelling to an Asian country from Germany (Cologne-Bonn Airport) by a Turkish Airlines flight. My transit is at Istanbul. I will be carrying some calcium tablets with me in my hand luggage.

Is there any restriction from Turkish Airlines or airport Security for carrying medicine in hand luggage?

I did not see any such restriction at Turkish Airlines website.

Yes, you may. Turkish Airlines do not mention medicines as restricted items because they are not restricted items as far as they are concerned (with the exception of medical oxygen tubes, should you consider those 'medicine').

Medicines are though covered by the liquids rule ("3-1-1").

What you should watch out for is not the airline's regulations so much as those of the country/countries you are visiting in Asia, since import restrictions are far more likely to be relevant - sometimes for items generally considered innocuous (eg Codeine).

However calcium tablets (calcium carbonate and calcium acetate, often with a minty flavour) are essentially just chalk. There is hardly a less dangerous/addictive compound. Chemically it is very similar indeed to what teachers used to write on blackboards with. Would you expect a child carrying a box of chalks to have issue with this either on an aircraft or with Customs and Immigration? No, calcium tablets, provided you don't choke on them, are completely harmless.

Although pnuts has written a very clear answer, I'd like to add my experience. I've flown Turkish Airlines many times, almost always had basic pills such as paracetamol in my handbag, and never had any problems neither at boarding nor at Istanbul Airport security control.