According to KCET eligibility criteria mentioned in https://engineering.careers360.com/articles/kcet-eligibility-criteria, if you have studied for a minimum period of 7 years in an Institution in Karnataka starting from your 1st standard to PUC, then you are eligible for domicile of Karnataka. Because you have studied for 8 years and your mother is a resident of Karnataka, you are eligible for appearing for KCET. As a proof of document, you will need your Study certificates as a proof that you studied in Karnataka for 8 years.