Yes----strictly from an income tax standpoint, your fiance could claim the children, get Head of Household filing status and get child-related credit like the child tax credit---which you cannot get since you did not earn enough to get CTC. But we have no idea how BF claiming the children would affect their medicaid. If you lived together all year and your income for 2023 was less than $4700, BF can even claim you and get the $500 credit for other dependents for claiming you. Would that affect medicaid? We do not know.
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