Greetings,

Even though you  choose for private colleges in your choice filling the counselling is conducted by the state government(UP). the seat that is allocated for you from this counselling whether it is a government college or private college it comes under the state government quota even it is a private college they should follow the fees structure provided by the government and it will be way too less than it compared to the management quota that is why you are paying the security deposit.

even if you don't want to participate in the counselling after you have paid the deposit you can get the amount refunded form the nodal centers.

hope this is helpful thank you