What should I do?

I have worked in a new place for more than one month. At On the first day when I worked here, my boss had an interview with me. He asked me: have you done completed all your jobs in your previous company? "Sure, almost all cases have been done except the one that my previous boss hoped me I would finish it at before the end of this year." "Who pays you? I hope you only work for my group in your all work time.," Mmy new boss answered me.

I wrote a letter to my former boss with some excuses, which were time limited limits, no ideas and others. I supposed my former boss would accept my request reasons. To my surprise, he replied to me that the time could be extended to for more two more months. Omg, wWhy do I have to do that?
Both of my bosses are the ones people I respect very much. The reason I did not refuse the requirement from my former boss is that he helped me a lot and the new boss is the one someone he introduced to me. He is a really nice guy and helped me selflessly like I'm his daughter.

Do you have new other ideas that could help me solve this issue? Many thanks!

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The first thing to understand is that your former boss is doing the wrong thing.  He has no right to ask you to do a job.  You must say no again.  It may help if, in your letter, you give him some tips about how your replacement might complete the job.  If you do this, write the letter on your day off from work.  In this way, you will be doing the right thing by your former boss (by providing him with a little guidance), and doing the right thing by your current boss (by not doing 'other' stuff when you should be working).

I want to repeat that your former boss is doing the wrong thing in asking you to do a job.  You are doing the right thing in saying no to him.  You must say no again.  Good luck!