Hello, this is Jennifer and thank you for requesting me.
The chances for getting your green card depends on you qualifying for an actual basis to get it. Unfortunately there is no basis for a green card from just sending a letter to the President. That would be something you used if your application was delayed or you needed a pardon for a crime. In your situation, a President cannot help to revive an I-140 that has been denied especially due to employer's issues. What you would have to do is have your employer file a new I-140 or find another employer that will submit an I-140 for you. You do not need to work for them right but if you want to then you could switch your H1B over to them. That will be the easiest.
The other ways to get a green card are limited and are:
1. The most common way is through your family. It must be through what is called immediate relatives that must be US citizen or legal permanent residents. These would be your spouse, your parent or your child if they are 21 and over, or also through a sibling... If you have one of those, they can petition for you to come to the US. It doesn't sound like you have any of those at the moment. Your child can petition for your green card once she turns 21. If you are in the US at that time, you must be in a current valid status to get your green card.
2. Investing in the US is another way to get your green card here. If you can invest at least $500,000 in a company in the US, there is a special green card program.
You would also have to create 10 or more jobs for U.S. workers through this investment.
3. The next way is applying for asylum.
You must prove that if you returned to your home country, you will be persecuted there on account of your religion, race, nationality, religion, or membership in a particular social group.
You would have to show that you would be persecuted for the reasons I listed. It has to be something that is happening only to you or a small group and not to the general population. You would have to apply for this within 1 year of entering the US.
5. The last is through the diversity visa.
6. If you were ever placed into immigration court proceedings and saw a judge in danger of being depoarted, you can request something called Cancellation of removal, where if you win you are given a green card. This is available to people that have been here at least 10 years consecutively, have a US citizen spouse or child, have been people of good moral character. However to actually win, their spouse or child who is a US citizen must suffer extreme and unusual hardship if you are deported. To prove that, usually the spouse or child has to have a serious medical condition for which they are receiving treatment in the US. If you dont have the medical issue part, it is not worth the risk because you will likely not win.
Besides this, unfortunately there aren't any other ways to get a green card.
Good luck to you during this process and I hope this answer has helped you!
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