Here are some of the colleges name you can prefer.

Indian Institute of Technology, Goa through JEE Advance

BITS Goa- through BITSAT

NIT Goa- through JEE Main

GOa college of Engineering- GCET

Shree Rayeshwar Institute of Engineering and Information Technology through GCET

Good Luck!

Below are the colleges in Goa for B.tech-



National Institute of Technology, Goa

BITS Pilani, Goa Campus.

Goa College of Engineering, Farmagudi



To check all the colleges in Goa you can refer below link-



http://www.engineering.careers360.com/articles/top-engineering-colleges-in-goa-2015