After being lured to New York two years ago to help revive the city’s subway, Andy Byford earned praise from riders and mass transit advocates for bringing about improvements on an antiquated system that had been undermined by breakdowns, delays and mismanagement. Mr. Byford has now resigned, sowing doubt about the future of extensive plans that are intended to modernize the nation’s largest subway system. Mr. Byford suggested in his resignation letter that he had chafed over a plan supported by the governor to scale back his duties as part of a reorganization for the Metropolitan Transportation Authority, the state agency that runs the subways and is controlled by Governor Cuomo. Mr. Byford’s colleagues at the M.T.A. believed Mr. Byford’s high profile may have irked Mr. Cuomo. The governor’s aides said that Mr. Byford often tried to take credit for improvements that were unrelated to his own work. Over the last year, the two men quarreled over plans to fix the L train, a major line between Manhattan and Brooklyn, and new technology to upgrade signals. Mr. Byford came to New York after leading the subway in Toronto, where he won an award for transit system of the year from the American Public Transportation Association. He has also worked on both London and Sydney’s transit networks.