Good afternoon John,
I'm Doug, and I'm very sorry to hear of your situation. My goal is to provide you with excellent service today.
No, social security does not award fractional quarter credits.
Social security no longer gives credits based on quarters but based on income earned during any time of the calendar year. The amount of earnings required for a quarter of coverage (QC) in 2016 is $1,260. So if your wife can earn income and pay taxes on $5,040 in 2016, she will have earned the 4 quarters. She does not need to work all year. In fact if she has a job paying that much in one day, then working just the one day is sufficient to earn the 4 quarter credits.
You can refile self employment tax returns going back only 3 years----but you will probably raise a red flag as to what happened and why you are now showing greater income. In other words, why didn't she report he actual income to begin with----but yes, it would work.
Social security does not apply earned credits until the following year when you file your tax return, so she will not be eligible for disability in 2016 unless you can show extra credits through tax return amendments for prior years.
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I wish you and yours the best in 2016,