POWER OF ATTORNEY

        KNOW ALL PERSONS BY THESE PRESENTS, that the undersigned hereby makes,
constitutes and appoints Usman Shakeel as the undersigned's true and lawful
attorney-in-fact, with full power and authority as hereinafter described on
behalf of and in the name, place and stead of the undersigned to:

        (1)   prepare, execute, acknowledge, deliver and file Forms 3, 4 and 5
(including any amendments thereto) with respect to the securities of EVO
Payments, Inc., a Delaware corporation (the "Company"), with the U.S. Securities
and Exchange Commission (the "Commission") and any national securities exchanges
or similar authority, as considered necessary or advisable under Section 16(a)
of the Securities Exchange Act of 1934 and the rules and regulations promulgated
thereunder, as amended from time to time (the "Exchange Act");

        (2)   seek or obtain, as the undersigned's representative and on the
undersigned's behalf, information on transactions in the Company's securities
from any third party, including brokers, employee benefit plan administrators
and trustees, and the undersigned hereby authorizes any such person to release
any such information to the undersigned and approves and ratifies any such
release of information; and

        (3)   perform any and all other acts which in the discretion of such
attorneys-in-fact are necessary or desirable for and on behalf of the
undersigned in connection with the foregoing.

        The undersigned acknowledges that:

        (1)   this Power of Attorney authorizes, but does not require, each such
attorney-in-fact to act in their discretion on information provided to such
attorney-in-fact without independent verification of such information;

        (2)   any documents prepared and/or executed by any of the attorneys-in-
fact on behalf of the undersigned pursuant to this Power of Attorney will be in
such form and will contain such information and disclosure as such attorney-in-
fact, in his discretion, deems necessary or desirable;

        (3)   neither the Company nor any of the attorneys-in-fact assumes (i)
any liability for the undersigned's responsibility to comply with the
requirements of the Exchange Act, (ii) any liability of the undersigned for any
failure to comply with such requirements, or (iii) any obligation or liability
of the undersigned for profit disgorgement under Section 16(b) of the Exchange
Act; and

        (4)   this Power of Attorney does not relieve the undersigned from
responsibility for compliance with the undersigned's obligations under the
Exchange Act, including without limitation the reporting requirements under
Section 16 of the Exchange Act.

        The undersigned hereby gives and grants each of the foregoing attorneys-
in-fact full power and authority to do and perform all and every act and thing
whatsoever requisite, necessary or appropriate to be done in and about the
foregoing matters as fully to all intents and purposes as the undersigned might
or could do if present, with full power of substitution and revocation, hereby
ratifying all that such attorney-in-fact, or such attorney-in-fact's substitute
or substitutes, of, for and on behalf of the undersigned, shall lawfully do or
cause to be done by virtue of this Power of Attorney.

        This Power of Attorney shall  remain in full force and effect until the
earlier of (i) the date on which the undersigned is no longer required to file
Forms 3, 4 or 5 with respect to the undersigned's holdings of and transactions
in securities issued by the Company; (ii) as to the appointment of Usman
Shakeel, upon his resignation or termination as an employee of Madison Dearborn
Partners, LLC; and (iii) revocation of this Power of Attorney by the undersigned
in a signed writing delivered to each of such attorneys-in-fact.  This Power of
Attorney may be filed with the Commission as a conforming statement of the
authority granted herein.


                               *   *   *   *   *


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


MADISON DEARBORN PARTNERS, LLC
MADISON DEARBORN PARTNERS VI-A&C, L.P.
MADISON DEARBORN CAPITAL PARTNERS VI-C, L.P.
MADISON DEARBORN PARTNERS VI-B, L.P.
MADISON DEARBORN CAPITAL PARTNERS VI EXECUTIVE-B, L.P.
MADISON DEARBORN CAPITAL PARTNERS VI-B, L.P.
MDCP CARDSERVICES, LLC
MDCP VI-C CARDSERVICES BLOCKER CORP.
MDCP VI-C CARDSERVICES SPLITTER, L.P.
SAMUEL M. MENCOFF
PAUL J. FINNEGAN

By:  /s/ Annie S. Terry as attorney-in-fact