Can I migrate to a different college after completing my 1st year of BBA at Christ University?

Yes, it is possible to change your college after completing your BBA 1st year from Christ University. 

I got selected at Christ University, Bangalore for a BBA in Finance and International Business but a year later, my father got transferred to Chennai, and there I completed my BBA. 

The admission process for transferring to another college depends upon the policies of your desired college/university you wish to join. If you wish to join another college in 2nd year, visit the official website of the college you want to enrol yourself in and get well acquainted with the admission details, eligibility for your case and most importantly check whether they have seats available for the BBA program or not. 

I would suggest directly calling the admission office or your desired college/ admission or visiting the college campus if possible, they would provide you with the necessary information for transfer admission. 

Some important documents that are required to transfer from college are a Transfer Certificate, Migration, Non-Objection Certificate (NOC) one from your desired college and another from your own where you study, your scorecard of 1st year and then your documents plus mark sheets (10 and 10+2). Please note that eligibility and document requirements vary.