As you said you are from Bihar, you do not have a domicile certificate for the state of Uttar Pradesh. Only domicile holders of a particular state are eligible for the state counselling (85% state quota) of that state. Rest of the 15% seats are available through All india quota

So you have two options-

1. If you want a government college, you must apply for All India Counselling and lock the choice of college you want

2. If you are willing to take admission in private medical colleges of UP, you can register for state counselling there (selecting your state as other state ). Note that you will only be eligible for management seats in private colleges.