Two city workers stole at least $340,000 intended for the neediest New Yorkers to enrich themselves and their accomplices — with one alleged fraud continuing unchecked for six years, authorities charged Thursday.

In the case going back to 2009, Human Resources Administration staffer Harry Fletcher allegedly gave away food stamps to ineligible cronies in exchange for kickbacks of up to $200 a month, according to the Department of Investigation.

Fletcher, 44, who was able to register his accomplices for public benefits without proof of eligibility, allegedly bragged to one cohort that “I’ve been rocking this for years.”

Nine of his alleged accomplices, including a city’s public-hospitals worker, were charged with defrauding HRA of between $18,800 and $35,000 each, officials said.

In a separate case, Staten Island HRA clerical worker Peter Ransome, 60, was charged with siphoning more than $90,000 in public-assistance funds for pal Jenneha Cooper. The suspects were hit with charges ranging from grand larceny and fraud to theft of government funds, officials said.