City and state officials on Tuesday announced measures to address New York City’s overwhelmed summons-courts system and ease a backlog of criminal cases that keep thousands of people jailed for months on end while they await trial or resolution of their charges. Changes to the city’s summons courts will include a redesign of the paper summons form police hand to people accused of violations, a new reminder system to get defendants to make their court appearances, online-payment options and more flexible appearance dates and times, according to officials from City Hall and the state court system.