Served 1 month of 2 month notice period termed as absconded

I recently resigned from my job and got approval of the same. I was to serve 2 months notice as per my appointment letter but the new company insisted on doing only 1 month and opportunity was good so, I approved of this. I talked my HR regarding payout as there was clause regarding the same to payback. But, he denied saying that it is in company discretion to accept payback. I served 1 month and joined the new company before informing the previous employer that I will not be able to continue due to some personal reasons. I got a reply from HR that it will not be accepted and will be termed as absconding and no relieving and experience certificate will be issued. My question is can they deny me relieving and experience letter? My new HR is confident that they will issue the certies. But my query is that if after 1-2 month of joining the new company I am not able to get the certies can I be asked to leave by the new employer and if there is any way of getting certies from my previous employer? I am very tensed and unable to concentrate on new job please reply