Denial of noc by institute, stated that according to our service record you are not eligible for job

Submit your application to Head of Deptt. to reconsider  your request with relevant records.

Your situation is quite complex, but there are a few possible approaches you can consider:

Clarification and Appeal – Since your post-graduation degree and prior work experience were omitted due to a bonafide mistake, you may request your office to reconsider your case.

You can provide documentary proof of your qualifications and experience and formally appeal the decision. Legal Precedents – There have been cases where courts have ruled that NOCs cannot be denied on technical grounds if no public interest is involved.

You may want to check if similar rulings apply to your case. Administrative Tribunal or Legal Action – If your office refuses to update your service record and denies your NOC, you may approach the Central Administrative Tribunal (CAT) or seek legal counsel to challenge the decision.

Higher Authorities – You can escalate the matter to a higher authority within your department or ministry, explaining the circumstances and requesting an exception. Alternative Approach –

If updating your service record is not possible, you may explore whether the new employer can accept self-attested documents or other proof of your qualifications and experience.

 Since this is a legal matter, consulting a lawyer specializing in service law would be beneficial. You can find more details on similar cases here. Hope this helps!

There is no rule that service can be added only during probation. 

Have you met a higher officer?

You can submit a written representation to the competent authority through proper channel and get their reply denying the request in writing after that you can approach CAT or directly to high court with a writ petition (considering the urgency) seeking direction to your competent authority to grant NOC, if it is wirhtin the rules.

You have to make request at every level.

they have unquestionable discretion to disallow (and even allow) ex-post facto permission. If permission is denied in that case you are not allowed to use this qualification for promotion / deputation/ forwarding application to deptt, for all times to come.