Hi Sameeksha,

B.Sc - B.Ed integrated course is a 4 year course offered by some universities across India. Admissions in most of the colleges is done through your board marks or any other entrance exam.

Looking for recognised universitries that offer this course, 

Lovely Professional University, Phagwara

Sharda University, Noida, etc are some. 

As the course is new, these universities that offer the course would give quality education. It depends n how much interested you are in the subject. 

Most of these universities start their phase 1 application by the first week of January every year. 

Keep checking the official website of the universities that you prefer. 

All The Best