Biometric Verification for Entry and Reconfirming Identity with Forensics Act of 2023 or the B-VERIFY Act of 2023 This bill addresses various immigration-related issues, including by imposing penalties on parents of unaccompanied alien children who arrive in the United States. Under this bill, any applicant for an immigration benefit, including a U.S. national applying for a non-U.S. national ( alien under federal law) beneficiary, must provide biometric information, including DNA. Furthermore, before the Department of Health and Human Services (HHS) may release an unaccompanied alien child to a sponsor, the potential sponsor must undergo a background check that includes certain searches, including a Federal Bureau of Investigation National Criminal History Check. (HHS currently conducts background checks of potential sponsors, but is not required to conduct all the checks required by this bill.) HHS must report a potential sponsor to U.S. Immigration and Customs Enforcement (ICE) if the potential sponsor (1) fails to prove a claimed familial relationship with the child, or (2) provides a false identity document. HHS may not use government funds to provide legal counsel to detained unaccompanied alien children. The bill also imposes penalties on the non-U.S. national parents of an unaccompanied alien child who arrives in the United States, including by deeming the parent inadmissible into the United States if the parent does not have lawful permanent resident status. Federal employees must promptly notify ICE if they receive an identification document indicating that an individual is unlawfully present. ICE must promptly place the individual in removal proceedings.