Hi

Get and No-Objection-Certificate from both the colleges. They will tell you that seat transfer is possible, but not branch transfer

Approach the governing body governing both of your colleges. Like AICTE for most cases(I might be wrong here)

After following necessary steps mentioned by the body. Your seat transfer procedure might be initiated.

No backlogs and no fee due are rules of thumb.

In case of private colleges, you need to pay the remaining years fee in your present college and then leave.