As you are from West Bengal, you need to apply WBJEE to get good engineering colleges as you mentioned just only of your HS.

Best colleges in West Bengal via WBJEE :

Jadavpur University

IEM, SALTLAKE

Heritage Institute of Technology

Kalyani Government Institute of Technology

Techno India, Saltlake

JALPAIGURI GOVT institute of Technology

St. Thomas Institute of Technology, Khidirpur

Haldia Institute of Technology

Rcc Institute Of Technology

BP Poddar Institute of Technology

Good luck!

These are some of the top government and private college in West Bengal:-

 

• Indian Institute of Technology Kharagpur
• Indian Institute of Engineering Science and Technology Shibpur
• Jadavpur University, Kolkata
• Maulana Abul Kalam Azad University of Technology, Kolkata
• Indian Institute of Science Education and Research Kolkata
• Haldia Institute of Technology, Haldia
• Institute of Engineering and Management, Kolkata

 

All the very best and good luck.

I would suggest you to go through with the given below link to check the top colleges in West Bengal & the eligibility to apply.

Top Engineering colleges in West Bengal

 

Good Luck!