discuss the issue with the person you mentioned, he will be helpful to you, as he is the only person who can make the HR recorded that you have reported him on the date as mentioned by you
In theory legal remedies exist, but in practise, the delays and issues which will come up if you take legal approach make it counter productive.
Seek a meeting with HR head and try to convince him.
If you have joined them on September 11 and continuosly worked with them (including transfer) you should be paid from September 11 to September 30.
You can do the below mentioned :
1.Collect all evidences of working during the said period like attendance records (if possible),mail communication in respect of work with team members and client representatives etc.
2.Report the matter to your Principal employer.They might apply pressure on your contractor to pay you in accordance with actual date of joining.
3.Escalate the matter to the highest authority in the company with proper details and evidence.
4.Threathen your employer that you would lodge complaint with the Labour Commissioner.
5.But firstly ensure that your original educational marksheet is derived from them.
Note: You are lucky to get appraisal, if your DOJ was from 1st Oct then you would have lost it. Most of the companies follow this.
One thing is not clear to me - 11th Sept. is't the real DOJ on which you reported to duty to your office or simply the date by which you should have joined your office. What is actual date you joined, punched your attendance/fed your biometric attendance. If both are different dates then there should be clarity. You are entitled to salary from the date actually you reported. Did you give any joining report, whether it was acknowledged ? It's obvious/it's normal there used to be a few days delay to get your access code/card. Many a time the attendance is linked to the electronic data thru' the bio-metric or access code. It's possible the pay roll has no provision to overlook these electronic data. In short, it's the duty of your reporting manager/lead /TL to set right this error. Probably instead of you directly tackling this issue with your outsource agency, your TL/manager should take it up with the concerned. Presumably your outsource agency might be not taking up your follow up for want of authentication from your HOD/TL/Manager. Pl.try this route.