LIMITED POWER OF ATTORNEY FOR SECTION 16 REPORTING OBLIGATIONS

Know all by these presents, that the undersigned James G. Welch, (the "Reporting
Person") hereby constitutes and appoints each of William M. Parent and Lauren B.
Messmore as the Reporting Person's true and lawful attorneys-in-fact to:

(1)	execute for and on behalf of the Reporting Person, in the Reporting Person's
capacity as a reporting person pursuant to Section 16 of the Securities Exchange
Act of 1934, as amended (the "Exchange Act"), and the rules thereunder of
Randolph Bancorp, Inc. (the "Company"), Forms 3, 4 and 5 in accordance with
Section 16(a) of the Exchange Act;

(2)	do and perform any and all acts for and on behalf of the Reporting Person
which may be necessary or desirable to complete and execute any such Form 3, 4
or 5 and timely file such form with the United States Securities and Exchange
Commission and any stock exchange or similar authority; and

(3)	take any other action of any type whatsoever in connection with the
foregoing which, in the opinion of such attorney-in-fact, may be of benefit to,
in the best interest of, or legally required by, the Reporting Person, it being
understood that the documents executed by such attorney-in-fact on behalf of the
Reporting pursuant to this Power of Attorney shall be in such form and shall
contain such terms and conditions as such attorney-in-fact may approve in her
discretion.

The Reporting Person hereby grants to each such attorney-in-fact full power and
authority to do and perform any and every act and thing whatsoever requisite,
necessary, or proper to be done in the exercise of any of the rights and powers
herein granted, as fully to all intents and purposes as the Reporting Person
might or could do if personally present, with full power of substitution or
revocation, hereby ratifying and confirming all that such attorney-in-fact, or
such attorney-in-facts substitute or substitutes, shall lawfully do or cause to
be done by the virtue of this Power of Attorney and the rights and powers herein
granted.  The Reporting Person acknowledges that the foregoing
attorneys-in-fact, in serving in such capacity at the request of the Reporting
Person, are not assuming, nor is the Company assuming any of the Reporting
Persons' responsibilities to comply with Section 16 of the Exchange Act.

This Power of Attorney shall remain in full force and effect until the Reporting
Person is no longer required to file Forms 3, 4 and 5 with respect to the
Reporting Person's holdings of and transactions in securities issued by the
Company, unless earlier revoked by the Reporting Person in a signed writing
delivered to the foregoing attorney-in-fact.

IN WITNESS WHEREOF, the Reporting Person has caused this Power of Attorney to be
executed as of this 2nd day of April, 2020.

/s/ James G. Welch