Regarding category 1a apply to my children for further studies

If you obtain appropriate community certificate having reservation as per your caste you can avail the privilege. 

Sir

thank you for kind reply

is it mandatory to study 10 years in Karnataka for eligibility to take seats in category quota for medical and engineering 

I have valid certificate and caste validity certificate also under same category I did Dental in Karnataka. Presently working in Maharashtra 

please guide 

Nothing prevented you from perusing the eligibility conditions as published in the brochure or application for admission for the course.

These are practical issues, if you have not understood the eligibility conditions you may revert with your doubts.

Each State has its own norms as to nativity of wards of of those residing/working outside their native States for one reason or other. You need to ascertain extant norms in the State of Karnataka.

Every State has prescribed caste(s) to extend benefit of reservation, consult area District Commissioner. 

Thank you sir