Yes, as per your say your fathers name is incorrect in your JEE main applicationso, the Jee main Always give some date for correcting the mistake in the JEE main application form.

But, if you miss the date you can contact to the JEE main helpline n.o as they will guide you properly

People spread instances where they face problems in haste, hence a lot of times we are scared about small problems like these. Go to your JEE MAINS application form(website) and you may find an option to edit the form. If not, it's not a very big deal, if the problem was in your own name, then it could've been serious, but in this case, it's just that your father's middle name has not been mentioned. So it's not a very big deal. Relax, hopefully you will not face a problem. I'm saying this because I faced a similar problem, but it was neglected.