This is a serious situation, and the HR's request is a major red flag. Submitting a resignation email under these circumstances means you are voluntarily resigning, which is legally very different from being terminated. This could allow the company to avoid providing you with a proper termination letter or a fair exit process.
Regarding your resume, you have two options:
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Do not show this experience: This is the safest approach if the tenure was short. However, be aware that this employment might still appear in your EPFO (Provident Fund) service history, which new employers check during BGV. Omitting it could lead to a "discrepancy" finding.
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Show this experience: This is risky, as the company is likely to give a negative reference. This could cause you to fail future background checks.
Your priority must be to protect your future. First, do not send the resignation email. Instead, ask HR in writing for the specific reason for the "negative" result and for an official termination/experience letter. If they refuse or give a false report, you can dispute it with your new employer using documentary proof like salary slips, Form 16, and your EPFO passbook. If they persist, consider sending a legal notice, as providing a false, reputation-damaging report may be actionable.