Procedure of Transfer of property from deceased father to only child (son), mother died earlier.

Mutation alone will not make you owner of the property. You may be the sole heir. But the world does not know that. If your father had left a will you should get it probated as the property is in Kolkatta. If your father had not left a will, you should apply for and get a succession certificate. You may hold on to the property without any of the above with no problem. But when you want to sell, the purchaser may or may not ask for the documents. If the purchaser asks for it, you will have to obtain it. If he does not ask you can sell it.  It is all your luck.