What is the process to call her as soon as possible?

Regrettably, there is no visa category by which a Permanent Resident my sponsor a fiance, and so other options would need to be explored. That may include, for example, any employment-based immigration applications for which your fiance may qualify, your application to become a naturalized citizen at the earliest possible time so that you then may sponsor her for immigration as a fiance of a U.S. citizen, becoming married in India and then applying for her in the family-based F2A visa category, etc. . There really is no substitute for you and your fiance 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.