Hi Ashish, first of all, PF and ESI are both separated. As you have said, "the employee wages are less and come under coverage of ESI." In your case, the problem is more difficult because of a 2-year duration.
So, your organization is very lucky, or the ESI officers in your state are not doing their job properly. Let's forget that and come to the point.
The current problems in your case:
1. You have not deducted employee contributions as well as employer contributions during that period.
2. Since you deducted PF amounts from those employees, you have definitely maintained their salary registers, and all bill payments done to the contractor are maintained in your account books too.
If an ESI officer audits your records at any time, you will be in trouble. They will impose a huge penalty on the company because the principal employer is always responsible.
Solutions that may be applicable:
1. Deposit all money, employee and employer contributions with a penalty. Send a forwarding letter to your ESI branch officer stating that since the employer doesn't have their code, you are depositing all the money with a penalty. Additionally, provide the ESI filled forms of employees and three duplicates with all employee details. Clearly mention that these employees have not faced any accidents up to the date of joining.
or
2. Whenever an audit takes place, try to hide all records related to that contractor (which is difficult since the payments are made to the contractor from your books with all details).
From now on, either apply for a new code or deduct the contributions and deposit them in your organization's ESI code with a separate challan.
Hope this helps you.