Issue a legal notice to your previous employer stating that it is all within my  right to resign and accordingly I have submitted my resignation which has been duly received by you. Hence the employment relationship has ceased to exist anymore. Further as I have joined another job I shall not be in a position to attend your office anymore. 

Further since I have not been provided any training I am not liable to reimburse any cost towards training. 

Also write to issue relieving letter immediately.

Now note that point 3 of your employment terms are totally illegal and void.  This can not be enforced by law. 

So don't worry. Join your new job without any tension.

If you face any problems or legal action by your previous employer , contact here for further advice and course of action. 

See you need to get your resignation letter and NOC if the immediate head is not accepting the resignation you need to contact and write to senior officials and ask for the acceptance of resignation. 

Hi

Your HOD should give reasons for not accepting your papers.

You need to escalate your issue to higher ups.

What ever you do, you need to keep copy of acknowledgement.

If you do not get response, get issued notice through an Advocate.

1) your employer is refusing to accept your resignation you would not get relieving letter 

2) since no training has been offered to you refuse to pay bond money 

3) take your job with govt if they don’t insist on relieving letter 

At the most you need to pay a one month notice about of your basic salary as you haven't served notice. Nothing more. You can file a complaint to office of dy labour commissioner. 

No since no salary received you do not have to pay anything for that.

Yes.you can intimate them of your resignation through mail or letter.

You should go office till you are not released by a letter or last date as per letter.

no training was given to you 

2) no question of payment of training costs arise 

3) don’t go to office as your new employer does not want relieving letter 

4) you can send scanned copy  through mail 

You should not go to your previous office.  You are no more an employee of that office. 

Just issue the notice as stated earlier. If you don't receive relieving order within a reasonable time issue another notice for the same giving 15 days more time to issue clearly stating that in default you shall be compelled to take appropriate legal actions.

if your new employer not asking relieving letter then don't go to office. you can send scanned copy through Email. 

Don't pay anything if they file any case it can be contested.Dont worry and relax

1.  Since you have submitted your resignation, just dont bother about the department's objection to this, as you are not going to claim any benefits out of this service, just ignore all those objections and proceed with your plan to quit the service and join the new employer, because they cannot obstruct your new employment by any means, at the maximum they can terminate your services, let them do it, it will hardly bother you.

2. You can follow the foot steps of the person who resigned his job prior to you.

You dont respond to their objections or any other form of threats.

They may not be able to do anything on this since your employment period is hardly a week and you were not benefited by this employment in any manner.

You may decide as you have proposed and leave the job without waiting for their nod, let them take any action on this which can be challenged legally as per law.

Dear

There is no need to pay any bond amount because the bond amount is for training provided to you and you havent get any training from them. 

You can leave the PSU and join you new employer if they don't need your relieving letter from previous organisation.

You can also send the resignation to senior officials for quick relieving.

HOD cannot force you to work for them if you are not willing to work.

1. As per the information mentioned in the present query, makes it clear that you have resigned as against the employment agreement, but still you do not come under the purview of training session and paying some percent of amount received.
2. If they happen to take any action then that would be of civil in nature which will not hamper your life or career.
3. You should contest it in the ground stated by you in the above query.
4. Keep all the communications about the resignation and their denial/ refusal for your future reply to their claim of any nature in future.