I have to take admission in NIT this year but I am currently admitted in Magadh University College If I cancel my admission from my current college am I eligible for NIT with a 1 year gap?

Yes, you are eligible for NIT, if you opt-out from Magadh University. First, you should cancel your admission and make sure that your admission at NIT is confirmed. 

My brother is a partial dropper and he joined NIT later. You will need to submit the gap certificate mentioning the reasons regarding the same. It is quite likely that they will accept your admission, despite the reasons you had. However, you will have to start from the first year. My brother informed the administration that he was preparing for IIT JEE while still studying at the college. The administration did not raise any questions. 

There are various partial droppers who joined the institution while still preparing for JEE side by side, and are now part of institutes like IIT, NIT, and BITS. So, you have nothing to worry about. Just focus on submitting the required documents and follow the necessary steps.

Now it is up to you what you want to give as the reason for your drop year. But it’s best to state the truth.