Your wage documents should be based on when you are actually paid, not when the payment was "earned." This is similar to deductions, you take them when actually paid, not when incurred or promised. (If you have a large medical expense but only pay a small part in 2015, you only deduct the amount paid, not the amount incurred.) If you are really paid on Jan 1, then those wages will be on your 2016 W-2. -- But note that if your employer writes the check and makes it available on 12/31, it will be on the 2015 W-2 even if you don't personally pick it up until after.
(That does not mean it is safe to file taxes based on your pay stub. There are a number of things that can change between your pay stub and your W-2, and if you don't get it right, you have to amend, which is a pain in the butt. But for estimating your taxes, you should figure that a check paid on Jan 1 will be on next year's W-2.)
