Hello,

If you get admission in presidency university and had admission earlier in Barasat Govt college , then it would be better if you cancel your admission by going to the college and also to check their site whether the admission and counselling fees is refundable or not. If you don't go to the college then your name will be automatically removed from their student list because you won't attending the college and they would simply understand that you have opt for the another college. But if you get your admission cancelled by yourself then it would be a responsible citizens move as you might get your fee back and you won't spoil the seat , in case of lateral entry admissions. 

So it would be better if you get your admission cancelled by yourself either by going through their site whether their is some procedure or not else you can directly contact college authority.

hope this helps