Since your fiancé and her children are not related to you in any way, you are not eligible for Head of Household filing status when claiming them as your dependents. Your filing status will be Single.
You would be eligible for receiving the Other Dependent Credit of $500 for each of them on your tax return if they meet all the rules for being a Qualifying Relative.
To be a Qualifying Relative -
1. The person cannot be your qualifying child or the qualifying child of any other taxpayer. A child is not the qualifying child of any other taxpayer if the child's parent (or any other person for whom the child is defined as a qualifying child) is not required to file an income tax return or files an income tax return only to get a refund on income tax withheld.
2. The person either (a) must be related to you or (b) must live with you all year as a member of your household.
3. The person's gross income for the year must be less than $4,700 (social security does not count) in 2023
4. You must provide more than half of the person's total support for the year.
5. The person must be a U.S. citizen or a U.S., Canada, or Mexico resident for some part of the year.
6. The person must not file a joint return with their spouse
See this TurboTax support FAQ for Head of Household filing status - https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-filing-status/qualify-head-household...
See this TurboTax support FAQ for what is a qualifying person - https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-filing-status/qualifying-person-head...
