Hi Fayeza,
Hope you are doing well. It is not necessary to provide a Domicile certificate since you have studied in Karnataka for so many years. But make sure that you carry the study certificate in the prescribed format from all the schools and colleges in which you have studied as it acts as a substitute or alternative to Domicile certificate. Study certificate is required for the proof that you have studied in schools in Karnataka. I hope you got the point after reading this answer.

All the best.