Regarding improper channel used for job change

It is always better to apply through proper channel but in your case you were denied as you are in probation.

Check the terms and conditions of your service during your probation period. I think that during probation period one can resign quickly and there should not be any problem on that account.

So you do not require a NOC also as you have not mentioned this job in SSC CGL application.

You may face some problems regarding your linkage of Provident Fund etc if that has been initiated in the present job. So you will not be able to link things from your present job to new job in absence of a valid NOC.

Your present job period will be a blank period as if unemoyed in your records in future.

You have done a mistake In case of government employment application giving wrong information is not correct. Once you are qualified the office will conduct enquiry. If they get the information about your employment , they may disqualify your candidature. I suggest it is better to mention in a separate letter about the present employment and mention the reason for not sending the application through proper channel. In such case they may consider for attending the selection process. You may inform the same to your present employer aldo.

If you were working in the private sector, the profile could be hidden. However, you cannot mess with government service. If you do so it is very likely that you may be terminated from the service. You may even be fined. Do understand that it is illegal and thus you may have to face termination, pay fine or in extreme cases may need to go to jail.

Applying through proper channel is a must. NOC certificate is a must and it can be obtained by filling an application form and then sending it to the higher authorities. Since your current employer has shown you a red flag, it is obvious that you are not eligible to take the step at least right now. The reason might be that you are bound by some form of a bond. In other cases, one can apply for a new job when in the probation period. You should read the rules and regulations to understand the things in a better way.

No, it would not be a fair step to suppress the facts before your current employer. While engaged in an assignment and going through the period of probation, it is illegal to apply somewhere else without letting it be known to your present employer.
You should approach the personnel - department and discuss the issues. You may put a proposal that the bond - money in the event of selection in the new assignment would be refunded back from your side. Hence, you may be allowed to apply for the new assignment. They may aceed to your request and you may get a NOC.

Under fear from your present employer you have gone for hiding of facts which sometimes is a risky proposition.

Now you have already applied there without any forward from the present office so in case you are selected there, you have no right to ask for NOC which is a crucial document in such situation.

So only option now is go ahead with the SSC CGL application and take leave during the exams and wait for the results before giving a notice for resignation.

Meanwhile you have to find the terms and conditions of the resignation in the present employment. That is an important aspect and you have to follow the procedure whether it is tendering one month salary in lieu of one month notice or whatever other regulations.

But I have intimated my current employer in writing that I am going to apply for SSC CGL. But they didn't reply to me till the time I filled the application and later they replied that you can resign and join the new one but couldn't be provided with any sort of permission or NOC.

Yes, you can apply for any other Government job while on probation. There is absolutely no bar. I am telling this with full responsibility.

You please submit your application online for SSC CGL Examination and submit a copy of the printout of the filled-up form to your office seeking the NOC for appearing in the examination. Please get your application acknowledged either getting a signature of the receiver in your personal copy or getting a computerized receipt number (FTS). If you don't get any answer in writing within 30 working days, you will take this as deemed acceptance and go on appearing the examination without any anxiety.

Check the CCS (Conduct) Rules and FR/SR minutely. Please go through Chapter 39 of the following link which deals with the forwarding of applications for another employment:-

https://dopt.gov.in/sites/default/files/1385465617HandBook%20for%20POs%282013%29.pdf