Understanding Your Company's Structure and Documentation
Firstly, I would like to know how many years the company has been in existence and how many full-time employees your company has. Is it that only a few cadres have not been given documents, or is it everyone? Is the company part of an unorganized sector/industry? Is it a proprietorship or a Ltd. company? These points are essential to provide a better view of the options that can be made available to you.
Proving Your Tenure to Another Company
Since you have been receiving the major chunk of your salary by check, you can simply furnish proof of bank statements for all the years.
Cash Component Inquiry
You state that a small amount is given as cash. Is it given as reimbursement towards any bills you provide? They would have definitely mentioned at the start what the cash component coverage is.
From the email, I presume that you have been working for 3 years, which means you have a comfortable salary, and perhaps the reason you are looking for documents now is that you wish to shift jobs.
Using Your Position as a Bargaining Factor
In which case, if you hold a strong position in the work profile of your company, you can use that as a bargaining factor. Request them that given your tenure, professional work conduct, and your future loyalty to the company, you would like them to at least provide salary slips, perhaps effective from January 1, 2014. (Out of all documents, this is the most important and has all relevant details to establish tenure, salary, leaves, name, etc.)
Hope this helps, and take a discussional tone with the management instead of a confrontational tone. I am sure they will at least hear you out.
Regards,
Deena Jagasia