No. They are not your sons so saying that they are would be fraudulent. If you and BF are not legally married then you are not a step parent.
If BF cannot claim his own children (no income?) then if the children lived with you ALL year you can claim then as dependents but only for the $500 credit for other dependents. You cannot use them as qualified dependents to file as head of household, and you will not get the child tax credit or earned income credit for them.
https://ttlc.intuit.com/questions/4499708-what-is-the-500-credit-for-other-dependents-family-tax-cre...
If you have your own qualified dependent related to YOU, then you can file as HOH. Otherwise you file as Single and claim the kids.
Am I Head of Household?
https://ttlc.intuit.com/questions/1894553-do-i-qualify-for-head-of-household
https://ttlc.intuit.com/questions/2900097-what-is-a-qualifying-person-for-head-of-household
If you qualify as Head of Household, when you enter your marital status (single or married filing separately) into MyInfo, and then enter your qualifying dependent, TurboTax will offer HOH as your filing status.
If BF had less than $4400 of income not counting Social Security and lived with you all year, he can also be claimed for the $500 credit.
**Disclaimer: Every effort has been made to offer the most correct information possible. The poster disclaims any legal responsibility for the accuracy of the information that is contained in this post.**
