Normally,it is supposed that lawyers demand money as per their wish to take a  case. Is that right or is there any rule/procedure to claim fees from client by a lawyer?

There is no such rule or restriction on fees of the advocate. Every advocate is at liberty to negotiate fees for his work considering his/her experience and standing practice depending upon the complexity of the matter. You can negotiate about the amount and if the fees quoted by the lawyer is not acceptable to you then, you are at liberty to take the services of another lawyer.

Correctly opined by Adv.Archana.

rightly advised by Ms. Archana

But after getting full & final fees in advance, an advocate keeps demanding extra money on every date then what one person  can do against this injustice?