hi,

see in Airport authority of India air traffic controller position recruitment, there is no condition given as you would be given time to complete your study and then join. its clearly mentioned that candidates whose final years results are awaiting are eligible to apply , on condition that they must produce the final marksheet or certificates at the time of verification. since you are only at third year of your integrated 5 years of  studies, you are not eligible to apply, even if you appear in exam, your candidature would cancelled at the time of verification.

now that you have to think, either you should try for this exam or focus on your college studies and later apply for other exams.