hi,

see game development comes under computer programming related courses, so you need to study courses related with computer technology, coding after you passed your 10+2 course, you may go for nay of the following course,

btech in information technology/computer science

bachelor in computer application

bsc in computer science

see from job prospect of view I suggest you to go for btech or bca courses. for btech course many state level and national level entrance exams held in india like jee main, wbjeeb, mhtcet etc, for bca course there is some university like amity, christ university has own entrance test, but most of the colleges takes admission based on 12th score.