It's complicated. I terminated my employment on 12/31/17 and was therefore not covered by a Retirement Plan in 2018. However, due to a stub payroll cycle, my ex-employer withheld and contributed one last 401k contribution in the first week of January 2018. So, I was not covered, yet the stub payroll shows a 401k contribution which shows up on my W-2. The fact is that I was not covered in a Retirement Plan in 2018 because I was not an employee. My AGI well-exceeds the income limits if I am viewed to be under a plan for some reason.
What I would like to do is contribute the difference between the maximum allowed and the stub 401k payment, and have my wife contribute the maximum, and have the sum of the two contribution be fully deductible--given that I was not covered by a Plan and therefore should have not income test.
If you were covered for one day in 2018 that is what the IRS uses. It goes by when you are paid, not when the work was actually done.
I fully understand what you are saying.
You would have to convince the employer to issue a new W-2 (corrected one) and have the retirement box not checked on it otherwise IRS will deny the IRA contribution.
"my ex-employer withheld and contributed one last 401k contribution in the first week of January 2018"
Terminating your employment at the end of 2017 does not necessarily make you not covered by that employer's retirement plan for 2018. If the employer's plan uses a fiscal year rather than a calendar year, since you made contributions for December 2017, you are covered for 2018. Your W-2 should reflect that by having box 13 Retirement plan marked; the IRS goes by the marking of this box. However, an elective deferral from your 2017 pay should have been reflected on your 2017 W-2, not on your 2018 W-2, so perhaps your employer has erred by showing this income and elective deferral on a 2018 W-2.
If the 401(k) plan uses a calendar year, you are not covered for 2018 and probably should not have received any W-2 for 2018. If the 401(k) plan uses a fiscal year rather than a calendar year, your 2018 W-2 probably should not show any dollar amounts unless you received some severance pay, but should have box 13 Retirement plan marked. I doubt that a 401(k) elective deferral would be permitted from severance pay, so it seems that there should be no elective deferral amount shown in box 12 of your W-2.