I have 3 yrs gap after 10th due severe illness. Can i give direct 12th privately after this?

Yes,you can do it anytime you wish to continue your studies by both mean correspondence and regular and also there are some other ways like NIOS & NWAC Boards where you can take admission.

It is too early for me to predict and for you to create anxiety worrying about your future prospects. Having said that I can assure you if you are well versed in academics, active cocurriculars and are focussed/passionate about learning break can be overlooked.

All the best!