Hello, Local certificate can be obtained if you have obtained education in that state consecutively for 4 years minimum. It can be proved with a resident certificate Whereas domicile certificate is obtained if you have become a resident there, it is more of a permanent in nature. You can avail home quota from NITK. To more details on reservation criteria kindly use this link https://engineering.careers360.com/articles/jee-main-reservation-criteria

Hope this helps.