Hello,
National Level Engineering Entrance Exams
S. No.Exam NameWebsite URL
1BITSAThttp://www.bitsadmission.com
2COMED-Khttps://www.comedk.org/
3IPU-CET (B. Tech)www.ipu.ac.in
4Manipal (B. Tech)www.admissions.manipal.edu
5VITEEEwww.vit.ac.in SRMJEEE www.srm.univ.ac.in
6AMU (B. Tech)http://www.amucontrollerexams.com/
7NDA Entrance with PCM (MPC)http://careerairforce.nic.in/index1.asp?lid=43&ls_id=50&level=3&lang=1&pid=38
8All India Engineering Entrance Exam with PCM (MPC)http://www.jeemain.nic.in
9State Level Engineering Entrance ExamsAndhra Pradesh - http://www.sche.ap.gov.in/eamcet/Eamcet/EAMCET_HomePage.aspx
Karnataka - http://kea.kar.nic.in/cet_2017.htm
Kerala - http://www.cee-kerala.org/
Maharashtra - http://www.dtemaharashtra.gov.in/approvedinstitues/StaticPages/HomePage.aspx
West Bengal - http://www.wbjeeb.in/
Chattisgarh - PET - Chattisgarh - PET
Gujarat - CET (B.Tech) - http://dte.gswan.gov.in/edte/
Jammu and Kashmir - CET (B.Tech) - http://www.jakbopee.org/index.aspx
Odisha - JEE (B.Tech) - http://ojee.nic.in/publicinfo/Public/View.aspx?page=71
Uttar Pradesh - JEE - http://www.jeecup.org/
You can visit these links to know in details regarding engineering entrance exams after 12th.
Good luck.

From 19th Jan, you have left - BITSAT, VITEE, SRMJEEE, KITEE etc..