Hello Eqtedar,

As you mentioned, 876 is a very good rank. You may get any college including the Bhagalpur college and Muzzafarpur Institute, Gaya Institute.

Go to the below link to check which all colleges accept your BCECE score.
https://engineering.careers360.com/colleges/list-of-engineering-colleges-in-india-accepting-bcece

You may not get top branches, at Bhagalpur University, such as mechanical and Electrical, but you may get CSE, etc.

You may try in other colleges such as Muzaffarpur Institute of Technology, Muzaffarpur , Bakhtiyarpur College of Engineering, Patna , Nalanda College of Engineering, Chandi , etc.

Hope this helps

Regards