If my mother filing for me, in what circumstances can I be denied?

Far more information is needed in order to provide a legal analysis of your eligibility for immigration benefits. This includes, for example, information about your mother's immigration status (is she a U.S. citizen? is she a Permanent Resident? does she have some other status?); information about you (How and when did you enter the U.S.? What is your current immigration status? What immigration-related applications ever before have been filed by or for you?; do you have a record of arrests, convictions, and so forth); Etc. There really is no substitute for you and your 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.