An 18 year old cannot petition for their parents.
US citizen can petition for an immigrant visa for their paren if the parent is outside the US or entered the US with a valid visa, but the US citizen must be 21 to do so.
The process to file for a parent who is residing abroad is for the US citizen to file an immigrant petition (I-130 and supporting forms, documents and filing fees) with the USCIS.
Once the immigrant petition is approved by USCIS they will forward the file to the Department of State National Visa Center. The NVC will sned the petitioner two fee bills. After the Petitioner has paid the fees the NVC will send the visa application and affidavit of support. When the completed forms and supporting documents are returned to the NVC the NVC will forward the file to the US consulate.
The US consulate will schedule an interview appointment for the parent. This will include a medical examination. Each consulate has a different procedure for how these interviews are conducted. The actual visa interview usually only lasts for a few moments. If the application is approved the parent will be given an immigrant visa packet either in person or it will be mailed to them.
Once the parent has the immigrant visa packet they can travel to the US where they will present the immigrant visa packet and be admitted to the US as a Permenent Resident. Their passport will be stamped as proof of their status and the green card will be mailed to them.
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Unfortunately Mr. Sauer is correct. Only children 21 years of age or older may petition for their parents. Your mother may have other options available for her to enter the U.S. You should consult with an attorney and discuss your full family history, your mother's immigration and biographical history and determine if there is another option for her.