There are no set guidelines as to why would an application be rejected and so we cannot be sure of whether you will receive your Admit card or not. But the possible instances in which any NEET application might be rejected are:

• If an incomplete application has been submitted.
• The same Candidate has submitted different application forms
• If the details mentioned in the application do not match with the document that you have uploaded.

Now in your case, it is your Father's name that has been mentioned wrong. Now entering your Father's name wrong will not affect the merit list. Agreed that you should mention the details as per the 10th marks sheet, but now, after the correction window has been closed, it is like being worried over spilled milk. We understand where your apprehensions are coming from. But when you filled up the application form, you also uploaded your 10th marks sheet and both the Application form and 10th marks sheet certainly have different names under Father's name column. But if you did not receive any notification or a mail from NTA regarding the uploaded document stating that there is a mismatch of details at both places, you are technically safe. So you should not be worried about this. NTA cannot over look the uploaded documents and that is why students get notifications regarding reuploading of uploaded documents. If you did not get any such notification, NTA must have considered it to be fine. So you do not have to worry about this.