You have chosen the EBACS (Economics, Business Studies, Accountancy, Computer science) in 11th and would like to take 12th standard in a correspondence method. 12th standarad is a very crucial step in the education pathway of a student. A good college, good marks etc help you to get enrollment into a good good UG course. A correspondence option at this stage would not be a wise decision. After 12th for you, you would be looking at B.Com, BBA, ICWA etc. Sometime back private PUC students face rejection for enrolment for UG courses in Bangalore university, you can please check that also.(https://www.thehindu.com/news/cities/bangalore/now-pu-private-candidates-cannot-pursue-higher-studies-in-bu/article6377017.ece)
Answering your queries
1.Is it possible to study (EBACS) 12th in correspondence?
Yes, it would be possible.
2.If it is possible then can you suggest where I can apply?
You can consider tutorials or coaching centers that can help you,
a. Prathiba Tutorials, Near Sumangali Choultry, Near Darga, Chickballapur, Gauribidanur, Chickballapur - 561208.
b.Apple Tutorials,Prabhakar Clinic Building, Girls School Road, Town Hall Sqaure, Chickballapur - 562101,
c.Akshaya Tutorials,Ward Number 22, Kodgibail, Chickballapur - 562101.
NIOS is a good option if you want to consider distance mode.In this site, 12th is referred to as Senior Secondary course. The minimum age is 15 years as on 31st July 2019.You should have passed 10th from a recognised board
Many people suggest IGNOU. In IGNOU, there is NO 12th standard enrolment. You need to enrol for BBP which is Bachelor's Preparatory Programme (http://www.ignou.ac.in/ignou/aboutignou/school/soss/programmes/detail/145/2), after this you can apply for a UG course.
Register as a private candidate in Karnataka for the PUC/12th standard. This link is form a government website (http://pue.kar.nic.in/PUE/PDF_files/exam/2019/private_2019.pdf) about private candidate enrollment guidelines. You can read this.
So, consider this information, you can also discuss with your 11 class teacher/principal and then come to a decision.