A year ago, I signed a contract with a company which last for a year. However after one year, the project wasn't finished in time so they asked me to stay for three more months. And there was supposed to be an extension contract but during that period the company was merging with another company and nobody was in charge of this affair. But I was still in the company's system and still got paid. So I did't say a thing about this. But now after I left, I got another job in another country. The immigration department need to verify all my previous working experience and ask for the soft copies of my contracts. I asked my former employer to get the contract and they agreed to send me one. The contract showed that effective date was from XXX to XXX which was two months earlier than current date. So how should I sign on the signature date? Is it a legal document for the immigration department?
Don't start making bogus contracts. Contracts that have been falsified in any way, such as having a falsified date, are invalid.
Ask your employer for a letter on official letterhead that states "[your name] was employed at [name of company] between the dates of [enter starting date] and [enter ending dates]." and make sure it is signed by an official agent of the company.
Provide the letter to the immigration department. That is proof of your employment.