<?xml version="1.0" encoding="utf-8"?>
<!--XBRL document created with Toppan Merrill Bridge  10.9.0.3 -->
<!--Based on XBRL 2.1-->
<!--Created on: 1/23/2025 12:08:35 PM-->
<!--Modified on: 1/23/2025 12:08:35 PM-->
<xsd:schema xmlns:srt-types="http://fasb.org/srt-types/2024" xmlns:xbrldt="http://xbrl.org/2005/xbrldt" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:link="http://www.xbrl.org/2003/linkbase" xmlns:us-types="http://fasb.org/us-types/2024" xmlns:xbrli="http://www.xbrl.org/2003/instance" targetNamespace="http://dime.com/20250123" elementFormDefault="qualified" xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:dtr-types="http://www.xbrl.org/dtr/type/2022-03-31" xmlns:enum2="http://xbrl.org/2020/extensible-enumerations-2.0" xmlns:deprecated="http://www.xbrl.org/2009/role/deprecated" xmlns:us-roles="http://fasb.org/us-roles/2024" xmlns:currency="http://xbrl.sec.gov/currency/2024" xmlns:ref="http://www.xbrl.org/2006/ref" xmlns:xl="http://www.xbrl.org/2003/XLink" xmlns:srt-roles="http://fasb.org/srt-roles/2024" xmlns:utr="http://www.xbrl.org/2009/utr" xmlns:us-gaap="http://fasb.org/us-gaap/2024" xmlns:sic="http://xbrl.sec.gov/sic/2024" xmlns:stpr="http://xbrl.sec.gov/stpr/2024" xmlns:country="http://xbrl.sec.gov/country/2024" xmlns:net="http://www.xbrl.org/2009/role/net" xmlns:naics="http://xbrl.sec.gov/naics/2024" xmlns:dei="http://xbrl.sec.gov/dei/2024" xmlns:negated="http://www.xbrl.org/2009/role/negated" xmlns:exch="http://xbrl.sec.gov/exch/2024" xmlns:attributeFormDefault="unqualified" xmlns:srt="http://fasb.org/srt/2024" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:dtr="http://www.xbrl.org/2009/dtr" xmlns:xbrldi="http://xbrl.org/2006/xbrldi" xmlns:dcom="http://dime.com/20250123" xmlns:rxp="http://xbrl.sec.gov/rxp/2024q3" xmlns:snj="http://xbrl.sec.gov/snj/2024" xmlns:us-gaap-ebp="http://fasb.org/us-gaap-ebp/2024">
  <xsd:annotation>
    <xsd:appinfo>
      <link:roleType roleURI="http://dime.com/role/DocumentCover" id="DocumentCover">
        <link:definition>00090 - Document - Cover</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType roleURI="http://dime.com/role/DisclosureStandardAndCustomAxisDomainDefaults" id="DisclosureStandardAndCustomAxisDomainDefaults">
        <link:definition>99900 - Disclosure - Standard And Custom Axis Domain Defaults</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:linkbaseRef xlink:type="simple" xlink:href="dcom-20250123_pre.xml" xlink:role="http://www.xbrl.org/2003/role/presentationLinkbaseRef" xlink:arcrole="http://www.w3.org/1999/xlink/properties/linkbase" />
      <link:linkbaseRef xlink:type="simple" xlink:href="dcom-20250123_def.xml" xlink:role="http://www.xbrl.org/2003/role/definitionLinkbaseRef" xlink:arcrole="http://www.w3.org/1999/xlink/properties/linkbase" />
      <link:linkbaseRef xlink:type="simple" xlink:href="dcom-20250123_lab.xml" xlink:role="http://www.xbrl.org/2003/role/labelLinkbaseRef" xlink:arcrole="http://www.w3.org/1999/xlink/properties/linkbase" />
    </xsd:appinfo>
  </xsd:annotation>
  <xsd:import namespace="http://xbrl.sec.gov/dei/2024" schemaLocation="https://xbrl.sec.gov/dei/2024/dei-2024.xsd" />
  <xsd:import namespace="http://www.xbrl.org/2009/role/negated" schemaLocation="http://www.xbrl.org/lrr/role/negated-2009-12-16.xsd" />
  <xsd:import namespace="http://www.xbrl.org/2009/role/net" schemaLocation="http://www.xbrl.org/lrr/role/net-2009-12-16.xsd" />
  <xsd:import namespace="http://www.xbrl.org/2003/instance" schemaLocation="http://www.xbrl.org/2003/xbrl-instance-2003-12-31.xsd" />
  <xsd:import namespace="http://xbrl.org/2005/xbrldt" schemaLocation="http://www.xbrl.org/2005/xbrldt-2005.xsd" />
  <xsd:import namespace="http://www.xbrl.org/dtr/type/2022-03-31" schemaLocation="https://www.xbrl.org/dtr/type/2022-03-31/types.xsd" />
  <xsd:import namespace="http://fasb.org/us-gaap/2024" schemaLocation="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd" />
  <xsd:import namespace="http://xbrl.sec.gov/rxp/2024q3" schemaLocation="https://xbrl.sec.gov/rxp/2024q3/rxp-2024q3.xsd" />
  <xsd:import namespace="http://xbrl.sec.gov/snj/2024" schemaLocation="https://xbrl.sec.gov/snj/2024/snj-2024.xsd" />
  <xsd:element name="FixedToFloatingRateSubordinatedNotesMember" id="dcom_FixedToFloatingRateSubordinatedNotesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="true" />
</xsd:schema>
