I submitted my research article to journal A earlier. They neither responded to my submission nor sent me any confirmation of my submission. I mailed them for the withdrawal of our submission. They did not respond to that email either. By that time I decided to submit my research to another journal B, which published my paper. The problem arose as journal A sent me an email regarding the acceptance of my submission. What should I do now to overcome this situation? Will it be considered as duplicate submission?
Remind them of the previous communications and insist that you already withdrew the paper. Provide copies if possible, with dates.
No, it isn't a duplicate publication, but make sure they understand that their "acceptance" is moot. It isn't required that your withdrawal be acknowledged for it to take effect since the rights to the paper are/were still yours.
I hope it isn't a case of your emails being sent to the wrong address and lost somehow. It would take some effort to clear that up. They might have been acting in good faith in that case.