How I can file a petition for my adopted mother?

Significantly more information is needed in order to provide a legal analysis of ways you may sponsor your adoptive mother for immigration benefits. That includes, for example, at what age were you adopted? Are you now a U.S. citizen? A Permanent Resident? Some other Status? Is your adoptive mother now located abroad? If your adoptive mother is in the U.S., what are the details about her entry into the U.S. and what is her immigration-related history? Etc. There really is no substitute for you and your adoptive mother to consult with an immigration attorney who, after learning all of the relevant information, could advise about eligibilities, options and strategies to attain your goals, and who then could offer legal representation in the often complex application process.