Your concerns on non-issue of payslip are justified. In this digital age if your company is relying on cash then it appears that the entire business is hidden from income tax authorities. But then is salary is disbursed to all the employees in cash or to you only? If all the employees are paid in cash then the business could be shady and you may leave this job and get into another job.
10th August 2015 From India, Bangalore
In my opinion, you may not be able to convince your new employer regarding your past employment. Whenever you get a new opportunity, explain the situation to new employer clearly and start as fresher. Anyhow the knowledge you will have got, surely will help you.
10th August 2015 From India, Kolkata