<?xml version="1.0" encoding="US-ASCII"?>
<!-- Generated by Broadridge Transform (tm) - http://www.broadridge.com -->
<!-- Created: Thu Jun 18 20:50:57 UTC 2026 -->
<xs:schema xmlns:ck0002128045="http://www.BleichroederAcquisitionCorp.III.com/20260618" elementFormDefault="qualified" xmlns:srt-types="http://fasb.org/srt-types/2026" targetNamespace="http://www.BleichroederAcquisitionCorp.III.com/20260618" xmlns:link="http://www.xbrl.org/2003/linkbase" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:us-types="http://fasb.org/us-types/2026" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xbrldt="http://xbrl.org/2005/xbrldt" xmlns:dtr="http://www.xbrl.org/dtr/type/2024-01-31" xmlns:xbrli="http://www.xbrl.org/2003/instance">
  <xs:annotation>
    <xs:appinfo>
      <link:linkbaseRef xlink:type="simple" xlink:href="ck0002128045-20260618_lab.xml" xlink:arcrole="http://www.w3.org/1999/xlink/properties/linkbase" xlink:role="http://www.xbrl.org/2003/role/labelLinkbaseRef"/>
      <link:linkbaseRef xlink:type="simple" xlink:href="ck0002128045-20260618_pre.xml" xlink:arcrole="http://www.w3.org/1999/xlink/properties/linkbase" xlink:role="http://www.xbrl.org/2003/role/presentationLinkbaseRef"/>
      <link:linkbaseRef xlink:type="simple" xlink:href="ck0002128045-20260618_def.xml" xlink:arcrole="http://www.w3.org/1999/xlink/properties/linkbase" xlink:role="http://www.xbrl.org/2003/role/definitionLinkbaseRef"/>
      <link:roleType roleURI="http://www.BleichroederAcquisitionCorp.III.com/role/DocumentAndEntityInformation" id="DocumentAndEntityInformation">
        <link:definition>000 - Document - Document And Entity Information</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
      </link:roleType>
    </xs:appinfo>
  </xs:annotation>
  <xs:import namespace="http://www.xbrl.org/2003/instance" schemaLocation="http://www.xbrl.org/2003/xbrl-instance-2003-12-31.xsd"/>
  <xs:import namespace="http://www.xbrl.org/2003/linkbase" schemaLocation="http://www.xbrl.org/2003/xbrl-linkbase-2003-12-31.xsd"/>
  <xs:import namespace="http://fasb.org/us-types/2026" schemaLocation="https://xbrl.fasb.org/us-gaap/2026/elts/us-types-2026.xsd"/>
  <xs:import namespace="http://www.xbrl.org/dtr/type/2024-01-31" schemaLocation="https://www.xbrl.org/dtr/type/2024-01-31/types.xsd"/>
  <xs:import namespace="http://xbrl.org/2005/xbrldt" schemaLocation="http://www.xbrl.org/2005/xbrldt-2005.xsd"/>
  <xs:import namespace="http://fasb.org/srt-types/2026" schemaLocation="https://xbrl.fasb.org/srt/2026/elts/srt-types-2026.xsd"/>
  <xs:import namespace="http://xbrl.sec.gov/sic/2026" schemaLocation="https://xbrl.sec.gov/sic/2026/sic-2026.xsd"/>
  <xs:import namespace="http://xbrl.sec.gov/spac/2026" schemaLocation="https://xbrl.sec.gov/spac/2026/spac-2026.xsd"/>
  <xs:element name="SponsorMember" type="dtr:domainItemType" abstract="true" xbrli:periodType="duration" nillable="true" substitutionGroup="xbrli:item" id="ck0002128045_SponsorMember"/>
  <xs:element name="MrGundlachMember" type="dtr:domainItemType" abstract="true" xbrli:periodType="duration" nillable="true" substitutionGroup="xbrli:item" id="ck0002128045_MrGundlachMember"/>
  <xs:element name="MrCombesMember" type="dtr:domainItemType" abstract="true" xbrli:periodType="duration" nillable="true" substitutionGroup="xbrli:item" id="ck0002128045_MrCombesMember"/>
  <xs:element name="BleichroederSponsor3LLCMember" type="dtr:domainItemType" abstract="true" xbrli:periodType="duration" nillable="true" substitutionGroup="xbrli:item" id="ck0002128045_BleichroederSponsor3LLCMember"/>
  <xs:element name="MJPAdvisoryGroupMember" type="dtr:domainItemType" abstract="true" xbrli:periodType="duration" nillable="true" substitutionGroup="xbrli:item" id="ck0002128045_MJPAdvisoryGroupMember"/>
  <xs:element name="PrivatePlacementWarrantsMember" type="dtr:domainItemType" abstract="true" xbrli:periodType="duration" nillable="true" substitutionGroup="xbrli:item" id="ck0002128045_PrivatePlacementWarrantsMember"/>
  <xs:element name="UnitsWarrantsOrdinarySharesMember" type="dtr:domainItemType" abstract="true" xbrli:periodType="duration" nillable="true" substitutionGroup="xbrli:item" id="ck0002128045_UnitsWarrantsOrdinarySharesMember"/>
  <xs:element name="NetProceedsFromThisOfferingAndTheSaleOfThePrivatePlacementWarrantsMember" type="dtr:domainItemType" abstract="true" xbrli:periodType="duration" nillable="true" substitutionGroup="xbrli:item" id="ck0002128045_NetProceedsFromThisOfferingAndTheSaleOfThePrivatePlacementWarrantsMember"/>
  <xs:element name="OfferingCostsAccruedForOrPaidInAdvanceExcludedFromTangibleBookValueMember" type="dtr:domainItemType" abstract="true" xbrli:periodType="duration" nillable="true" substitutionGroup="xbrli:item" id="ck0002128045_OfferingCostsAccruedForOrPaidInAdvanceExcludedFromTangibleBookValueMember"/>
  <xs:element name="AmountsPaidForRedemptionsMember" type="dtr:domainItemType" abstract="true" xbrli:periodType="duration" nillable="true" substitutionGroup="xbrli:item" id="ck0002128045_AmountsPaidForRedemptionsMember"/>
  <xs:element name="OrdinarySharesOutstandingPriorToThisOfferingMember" type="dtr:domainItemType" abstract="true" xbrli:periodType="duration" nillable="true" substitutionGroup="xbrli:item" id="ck0002128045_OrdinarySharesOutstandingPriorToThisOfferingMember"/>
  <xs:element name="OrdinarySharesForfeitedIfOverallotmentIsNotExercisedMember" type="dtr:domainItemType" abstract="true" xbrli:periodType="duration" nillable="true" substitutionGroup="xbrli:item" id="ck0002128045_OrdinarySharesForfeitedIfOverallotmentIsNotExercisedMember"/>
  <xs:element name="OrdinarySharesOfferedMember" type="dtr:domainItemType" abstract="true" xbrli:periodType="duration" nillable="true" substitutionGroup="xbrli:item" id="ck0002128045_OrdinarySharesOfferedMember"/>
  <xs:element name="OrdinarySharesRedeemedMember" type="dtr:domainItemType" abstract="true" xbrli:periodType="duration" nillable="true" substitutionGroup="xbrli:item" id="ck0002128045_OrdinarySharesRedeemedMember"/>
  <xs:element name="WithoutOverAllotmentMember" type="dtr:domainItemType" abstract="true" xbrli:periodType="duration" nillable="true" substitutionGroup="xbrli:item" id="ck0002128045_WithoutOverAllotmentMember"/>
  <xs:element name="WithOverAllotmentMember" type="dtr:domainItemType" abstract="true" xbrli:periodType="duration" nillable="true" substitutionGroup="xbrli:item" id="ck0002128045_WithOverAllotmentMember"/>
  <xs:element name="ShareholdersMember" type="dtr:domainItemType" abstract="true" xbrli:periodType="duration" nillable="true" substitutionGroup="xbrli:item" id="ck0002128045_ShareholdersMember"/>
  <xs:element name="InitialBusinessCombinationMember" type="dtr:domainItemType" abstract="true" xbrli:periodType="duration" nillable="true" substitutionGroup="xbrli:item" id="ck0002128045_InitialBusinessCombinationMember"/>
  <xs:element name="OfficersAndDirectorsMember" type="dtr:domainItemType" abstract="true" xbrli:periodType="duration" nillable="true" substitutionGroup="xbrli:item" id="ck0002128045_OfficersAndDirectorsMember"/>
  <xs:element name="ClassBOrdinarySharesMember" type="dtr:domainItemType" abstract="true" xbrli:periodType="duration" nillable="true" substitutionGroup="xbrli:item" id="ck0002128045_ClassBOrdinarySharesMember"/>
  <xs:element name="WorkingCapitalLoansMember" type="dtr:domainItemType" abstract="true" xbrli:periodType="duration" nillable="true" substitutionGroup="xbrli:item" id="ck0002128045_WorkingCapitalLoansMember"/>
  <xs:element name="spacTable" type="xbrli:stringItemType" abstract="true" xbrli:periodType="duration" nillable="true" substitutionGroup="xbrldt:hypercubeItem" id="ck0002128045_spacTable"/>
  <xs:element name="spacLineItems" type="xbrli:stringItemType" abstract="true" xbrli:periodType="duration" nillable="true" substitutionGroup="xbrli:item" id="ck0002128045_spacLineItems"/>
<!-- [WMV7][zXQKCosD5l1rHuIT8MATF5AJgdBZM0fWhzUsu4fkJk5WWsTxwVvjJCE2GdkJ4a96OkFN/EVJCiJXDa1RgMz8ZAjyRsLTTNdO5PZu0QPLAbrVWxGeRvmAxPwuJm4P9SOe/tcRkb3Y86bairPXvQ5Rdi/lPVJyZT7p8i7XtIbD6O2Pgp3fKHeg/D9lWllGs406fKy1E/bxlRKbeXfTsdJGTFH94v8pBKTx67MK7Cy41scjmBKKaSg4uLevJupme3L+mtryNwF7ouWEfWAWp6/AIEg6J8vAS4paBPs9d9NMUhDFEeGT6GBwlfGAf+wdLaCPFWcw3qiKcDOHM20aRD+8uckzlJHQceOlgjz5TCkAbWOy8cd1b885afIJQhhc2T1Wf4e/7O06PAWfSqE=] CSR-->
  <xs:element name="DocumentAndEntityInformationAbstract" type="xbrli:stringItemType" abstract="true" xbrli:periodType="duration" nillable="true" substitutionGroup="xbrli:item" id="ck0002128045_DocumentAndEntityInformationAbstract"/>
</xs:schema>
