You can file an appeal in the middle of a case so long as you are appealing from an actual decision. There is a $65 filing fee for filing the notice of appeal. You can make a poor person application to have this waived. You should look into legal aid or some other organization to help with as proceeding with something like this by yourself is very difficult.
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I would find an attorney to do a free consult with. Have you moved to have your husband pay your legal fees? Is your husband pro se as well? If not, you may be able to have him pay for your attorney. That being said, if there is a final ruling in your case you may be able to stay the ruling and file an appeal. Fees can be waived based on your financial situation. I would also call the local bar association for assistance.
Since you are on public assistance you may qualify for assigned counsel. Go to the Supreme Court in the county in which you live and ask for the application for assigned counsel. Specify that you also need counsel with appellate experience.
You can appeal an Order or Judgment, assuming you have one, as long as you were aggrieved in some way. You can apply to the Court to appeal on poor person's relief and you will not have to pay the fee, the transcripts or the attorney.
Here is some info on how to file an appeal in the Second Department:
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