Hi there. 

For the AIIMS PG examinations if all the seats of the centres of Kolkata are filled, then try applying for the centres of nearby cities like Patna, Howrah, Hooghly. 

You can even apply to other far away places like Delhi or Mumbai. 

You should reach the centres outside your city one day before the examination in order to reduce the stress of reaching the exam Hall late. 

Hope this helps.

Hello Promita,
For the AIIMS PG entrance exam, the city of examination shall be allotted on first come first serve basis. If all the centres of Kolkata are filled then you can choose any other centre from the available options.
Good Luck!