What is the capital of the city sham or shaam?

As far as I can tell, there is not a city called Sham and Shaam.  To make sure, I googled it and also looked in my very large (National Geographic) atlas.

Besides, cities do not have capitols.  A capital is the city where the government of a country (or an American state) is centered.

I think perhaps what you are thinking of is the country of Siam.  This was the name that was previously used to refer to the country that is now Thailand.  The capital of that country is Bangkok.