Randolph Bancorp (RNDB) 8-K/A Completion of Acquisition or Disposition of Assets

Exhibit 23.1

INDEPENDENT AUDIT FIRM’S CONSENT

We consent to the incorporation by reference in this Current Report of Randolph Bancorp, Inc. on Form 8-K/A of our report dated March 4, 2016, with respect to our audits of the consolidated financial statements of First Eastern Bankshares Corporation and Subsidiary as of December 31, 2015 and 2014, and for the years ended December 31, 2015 and 2014, which report appears in Randolph Bancorp, Inc.’s Registration Statement on Form S-1 filed with the Securities and Exchange Commission on March 4, 2016 as amended.

/s/ Marcum LLP

Marcum LLP

Boston, MA

September 15, 2016