how an andhra students can apply for the institute
Recommended: Want to Know Colleges, Specialization to Apply on the basis of your TNEA Rank? Start here- TNEA College Predictor
Yes you can definitely apply in Anna University as it has provisions for other state quota. They do have a limit for the amount of migrant students they take in, for example they have 16 (12+4) seats for southern India migrants. There may be slight variations depending on the subject you choose.
Admission to UG courses is granted on the basis of candidates' merit in TNEA ( Tamil Nadu Engineering Admission). TNEA application forms for the year 2019 are not out yet (for other state students) but they are suspected to come out in the third or fourth week of June. When the forms are out you can apply for the university here : https://www.annauniv.edu
Hope this helps :)