On the facts stated, you appear to have a reasonable basis to contest the proposed recovery.
The important distinction is between an error attributable to the employee and an error made by the organisation while issuing and implementing its own appointment/pay-fixation orders.
In your case, the 2021 interview/selection minutes apparently recorded that the appointment was to be made with continuity of service, and the competent persons approved the pay scale. The appointment order was then actually issued on that basis, with the same employee ID. If you neither supplied incorrect information nor concealed any fact, and you received salary strictly according to the organisation's formal order, it would be difficult to characterise the excess payment as something you deliberately or knowingly obtained.
The fact that the organisation now says that the 2021 appointment “should have been with a break” is not, by itself, sufficient. They should be able to identify the specific rule/order under which the appointment was required to be treated as a fresh appointment with settlement of earlier service, and explain why their own 2021 appointment order was issued differently.
The October 2021 informal meeting is also significant. If it was never communicated to you and was contrary to the written appointment/pay-fixation order, the organisation cannot simply assume that you were aware of it. The legal effect of those minutes would depend upon who recorded them, whether they were approved by the competent authority, and whether they were ever incorporated into or communicated through a formal order.
There is also an important issue regarding recovery of salary already paid. Courts have repeatedly distinguished between wrongful/unauthorised payment obtained by an employee and an administrative/pay-fixation mistake made by the employer, particularly where the employee had no role in the mistake and acted bona fide. Recovery is not automatically permissible merely because the employer discovers an error years later.
Since you have already resigned from the earlier post and your dues were settled, the organisation should also provide you with a written, itemised calculation of the alleged excess payment and the rule/order authorising the recovery, rather than simply adjusting an amount from your present salary.
I would therefore not advise voluntarily admitting the liability or agreeing to repay merely because the organisation has raised the demand.
A written representation should first place on record that:
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you were selected through the prescribed process;
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the 2021 minutes and appointment order provided continuity and the relevant pay fixation;
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the approved salary was paid by the organisation itself;
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you did not make any misrepresentation or conceal any information;
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the alleged October 2021 decision was never communicated to you;
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you acted throughout on the basis of the formal orders issued by the competent authority; and
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the organisation should disclose the statutory/service-rule basis, competent authority's order and complete calculation supporting the proposed recovery.
The exact appointment order, the 2021 selection/interview minutes, the pay-fixation order and the October 2021 minutes are particularly important here. Their wording can materially change the position, especially regarding whether the 2021 appointment was legally a promotion/transfer with continuity or a fresh appointment requiring settlement of the previous service.