Now both of you have differing interpretations of notice period.
The company is in a better position to dominate and ask for longer notice period(at least what was given in contract)
Suggest you go and negotiate with company and try for amicable exit.
Whereas regular employment contract, is normal appointment order with a specific clause for a notice period / in lieu of notice, for both parties to terminate the contract.
I am not in a position to understand your statement that 'My contract are ended' if so on what agreement / understanding the contract was given to you?
Going by your message it seems that you had entered into a time bound contract wherein a fixed from and to dates clause is on the paper and duly signed. Once the said period is over your contract also ends with no necessity for any notice to be provided, as you had successfully completed the period stipulated. If there is anything more to the employment letter, please do provide the details. Not sure as to why you had given them notice of 30 days.
Thanks and Regards
On completion of the Bond period if at all you want to leave the company, on normal course of business, there will a notice period which you have adhere.
As all our learned people have told, if it is a contract for a specific period then there cant be notice pay period, it may be there also if you want to leave the company before the contract period.
So in that case naturally only if you want to leave company before the contract period you may serve on the notice period.