If I am about to do my citizenship, can file for my mom even though she over stayed? Do she have to go back home during the filing process?

Generally, a naturalized U.S. citizen age 21 or older may sponsor a parent to adjust status to become a Permanent Resident in the "Immediate Relative" visa category, and may do this notwithstanding that the parent entered the U.S. lawfully and with inspection but then overstayed an initial visa. Of course, there are many other details that relate to immigration eligibility. It would be wise 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 - naturalization for you and adjustment of status for your mother and who then could offer legal representation in the often complex application process.