Can my next employer find out about this job through my PAN, PF, TDS or any other means?
To begin with, unless you are hired as an executive, a company spokesperson, or other "publicly significant" role, I highly doubt the new employer would care about the "hidden" job. However, if they are hell-bent on finding out, they can do it. They would not do it through your old PF or TDS records because of two reasons:
- It is tedious, time-consuming and expensive. The only way to legally access these records is by getting a court order, which is hard.
- There are other "unofficial" options to do it more easily.
They wouldn't go through a tedious legal process, when there are much easier means available:
- They just ask you and you tell them. (duh!?)
- They find out about your old employment from your social media profiles.
- They "accidentally" come in contact with one of your coworkers at
the old company.
It is easy enough for you to avoid 1 and 2. Just don't disclose your old PF and TDS records to them. For the purpose of the new employer's TDS, you will be deemed unemployed for those 3 months, even though you have paid income tax. Deal with that discrepancy while filing tax returns next year. Needless to say, don't use your new employer's tax consultancy service (if they offer one) to file the tax returns.
There can be no perfect strategy to avoid 3, because (for example) the HR or your boss at the new company could have a friend/spouse/sibling/etc. working at the old company, and their conversation could "accidentally" veer into talking about the new guy who joined last month.
Nonetheless, I would recommend you to avoid doing anything that arouses suspicion. Keep a low profile, focus on getting your work done, and do not say or do anything that draws attention to the 3-month gap. If you do your work well for a year or so, the new employer would have no reason to dig into an old gap.
They responded with a warning stating that ... they will declare me as an absconded employee ...
Although it was not professional to leave the job abruptly without notice, the fact remains that you have already done it and joined the new company. Your best option now is to ignore the warnings and move on from the old company. Since you have already made peace with not getting a relieving letter from them, there is nothing for you to gain by continuing the conversation with them.
For future reference, avoid leaving a job without notice. If you must do it, avoid leaving any paper trail (such as the email you sent to your old company). You would never know when it will come back to bite you.