In 12th and considering a career in research. Ik most of the collages ( IIT Kanpur, IISc Bangalore, IISERs etc ) but I am not sure of the research possibilities provided so if anyone can help out please do
Maths is available in every institute, be it IISER, IIT or the IISc. People also aim for ISI. If you are interested in pursuing a particular field in mathematics as your master's thesis, then look up the faculty profiles of each institute and check if there is at least one Professor pursuing research in that field. If there is no such restriction, focus on the entrance exam for now. Best of luck for the JEE! Also, don't forget CUET UG; you can always try IIT JAM after a BSc to get into IIT, or NET after MSc. CUET has some good institutes like JNU and DU.