They’re the masters of shamrock-and-roll.

Infamous Irish punk band The Prodigals tossed back a new type of Guinness Friday and partied at their equally famous home pub like it was 1997.

Paddy Reilly’s Music Bar threw a Celtic celebration in honor of its homegrown musicians — who secured the World Record for “longest annual residency by a band” after 29 years of dedicated weekly shows at the Kips Bay landmark.

The crowd roared when the band took the stage — and went even crazier when old members picked up their instruments in an ode to the nearly three-decade legacy they have etched into the Manhattan bar.

“I am absolutely delighted,” Gregory…

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