How did you get your green card? and how long ago? be prepared to show 5 years of taxes at the interview. Most likely you will be just fine. If and when you do get citizenship, in order to sponsor your mom, you have to be above the 125% poverty guideline - you can see the chart on uscis.gov, the form is I-864P
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You applying for rent-assistance will not effect your citizenship, nor will it effect you filing for your mother. However, if you do not meet financial requirements when filing for your mother, you will need to find a Joint Sponsor who will sign an Affidavit of Support for her. Good Luck.
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That should not give you problems, just be ready to prove that you meet the 125% of the poverty guidelines when you are ready to petition your mother.