What is the expiation for signing on behalf of some employees, without their knowledge or signature, with the aim of expediting the disbursement of the company's dues, knowing that the company has given the doer a financial reward, and he intends to donate the value of this reward, along with the difference in its value, after his repentance and remorse?

One must adhere to the conditions set by the state, for the Prophet, peace and blessings be upon him, said: "Muslims are bound by their conditions." If the company has violated the conditions for employing locals, then it is not permissible to assist it in circumvention. However, if it cannot find qualified individuals for the work, then there is no harm in its circumvention to obtain its right. Accordingly, the ruling on your work and your signing on behalf of others depends on the permissibility of the company's circumvention:

If the company's circumvention is legitimate because it is wronged, then what you did is permissible (halal), and the reward you received is permissible. However, if the company's circumvention is not legitimate, then it is not permissible to assist it, as this falls under cooperation in sin. In this case, if you were unaware of the prohibition, it is permissible for you to benefit from the reward. But if you were aware of the prohibition, then you must repent and donate the reward to the poor and needy, or give it to charitable organizations for the benefit of Muslims.

Ibn Taymiyyah stated that whoever acquires ill-gotten wealth and then repents: if they were unaware of the prohibition, it is permissible for them to consume it; but if they were aware of the prohibition initially and then repented, they should donate it.