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I mean is Self-Employed tax part of federal tax withholding?

federal withholding on your wages, assuming you file jointly, can be applied to her income tax liability and her self-employment taxes.

your other option is to pay quarterly estimated tax payments to cover her share of the income taxes and her self-employment taxes.

you would be a little late on estimated taxes 1/4  was due 4/18/22 and 6/15/22 with 1/4 due 9/15/22 and 1/16/23