Code J indicates that there was an early distribution from a ROTH IRA. The amount may or may not be taxable depending on the amount distributed and your basis in the ROTH IRA. TurboTax will walk you through some questions to determine if your distribution is taxable or not.
You should only include the Form 1099-R on your Tax Return for the year indicated on the actual Form 1099-R. The year is indicated in the upper right-hand corner of your Form 1099-R. Please click on the screenshot below for reference:
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The only Forms 1099-R that would need to be reported on tax returns for two consecutive years are those with code P in box 7 and that have nonzero amounts in both box 2a and box 4. This would include a Form 1099-R from a Roth IRA that includes both code J and code P in box 7. A Form 1099-R that has no code P in box 7 is only reportable on the tax return that corresponds to the year of the Form 1099-R.