Incorrect calculation of Full and Final Settlement

My last date was on Dec-10th and has submitted my tax proofs on Dec-6th which was validated and acknowledged by finance team before my LWD( taxable income is 0).
After one month, I received a mail on Full and Final settlement saying I have to pay 2 lakh rupees to company because of income tax.

when checked with team, they mentioned the investment proofs are considered in Jan month along with F&F. But, for Dec month the tax was deducted. So after calculating income tax and deducting 10 days Dec pay the overall amount is nearly 2 lakhs to be paid by me.

Company mentioned the tax deducted can be shown in New employer.

I need answers for the below questions.

1. I have submitted all the proofs in Dec month and still why the tax was deducted in Dec?

2. If my last date is on Dec-10th why the full and final settlement is done in Jan month.

3. Now I am looking for higher studies and do not want to file ITR and expected I will get 10 days and 25 leaves money as refund instead of paying 2 lakhs by me. Is this correct calculation?

Please provide some inputs on this.

If the company deducted and paid higher tax due to mistakes of its own internal procedure, it is the fault of the company and not yours. The law requires them to compute and deduct tax evenly through the year. In case you do not submit the tax proofs then in the last few months they can deduct higher. It is really stupid for someone to say they do not consider proofs given in December and will only consider it in February

It appears to me someone messed up and are trying to recover the money from you.

One thing you need to check is whether the money has actually been credited to your 26AS statement on the income tax website. that would mean the money is paid to the tax authorities and you can claim it back when you file your returns. Please remember that you need to file your returns in any case, even if you plan to study abroad.

How you deal with this is now up to you. You will need to show this experience later and it may create a problem in the BGV at that time. However, paying them ₹ 2 Lakhs is a heavy amount, specially when it will be at least a year before you get the refund from the income tax authorities.