First of all there is no such rule that a company will collect a duly signed blank cheque from its employee for any reason. It is illegal. The employee is not a borrower. He has not taken any advance from the company that he is bound to deposit a blank cheque with it.
The company's employment offer letter is to be seen to verify if the cheque or the said amount has been mentioned in it as an additional condition for the employment.
Generally it should be three months notice vis a vis by both the sides either for resignation or termination.
If you desire to resign the job for the cited reasons, you may tender your resignation by registered post with AD card to the Top management directly and not to the HR. HR is not the authority to approve and relieve you from the employment.
In the resignation letter itself you can very well mention about this blank cheque and demand to return the said cheque along with your relieving letter.
This evidence will help you to pursue the court case in this regard, if need be.