The city is accepting applications for it summer youth job program. Coordinated by the city’s Human Resources Department, the program provides employment to people age 17 to 21 in various city departments. This year’s program will run in two sessions. The first will be from July 8 to Aug. 2, and the second from Aug. 5-30. The city has budgeted $50,000 for the program, and Distrigas Suez, which operates a liquefied natural gas terminal on the Mystic River, has donated $25,000. The city is seeking a state grant to supplement the funding. Applications are available in the Human Resources Department on the third floor of City Hall. The deadline to apply is Thursday.