If you are not withholding social security and medicare taxes from the payments and matching the totals from the business account then you are treating them as an independent contractor, not an employee.
Paystubs are for employees. Any "paystub" showing $0 medicare & social security is a tell-tale sign of a business illegally classifying employees as contractors.
You can issue a payment statement with every check which documents how much is being paid and what the person is being paid for, but its not a paystub and shouldn't have fields for SS and Medicare. Its more like an invoice for payment for services.
At any rate, if you issue a statement, then it should be accurate for what was actually paid. If you withheld $0 for social security and medicare, then any statement showing those amounts should say $0 or else you're committing fraud by knowingly issuing an inaccurate statement.
The bottom line is that if you've misclassified the employees as contractors then you've created a huge mess and you need to hire professional accountanats (and maybe an attorney) to sort this out.
If the contractor destination is correct, then this person is self employed and their proof of income for a loan application or apartment or whatever should be their previous tax returns showing the income and copies of recent checks to prove the income is still flowing.