We investigate the environment in the vicinity of the supernova remnant (SNR) G59.5+0.1 and identify all the young stellar objects (YSOs) around the SNR, to derive the physical properties, obtain insight into the star-formation history, and determine whether SNR G59.5+0.1 can trigger star formation in this region. We perform the submillimeter/millimeter observations in CO lines toward the southeast of SNR G59.5+0.1 with the KOSMA 3m Telescope. High values of the integrated CO line-intensity ratio RICO(3-2)/ICO(2-1) is identified as one good signature of the SNR-MC (molecular cloud) interacting system. To investigate the impact of SNR G59.5+0.1 on the process of star formation, we use GLIMPSE I catalog to select YSOs (including Class I and Class II sources). The CO emission forming an arc-like shape and mid-infrared 8.28µm emission are coincident with SNR G59.5+0.1, which has a total mass of 1.1x104M☉ and fully covers the open cluster NGC 6823. Three molecular clumps are identified in the CO molecular arc, each clump tracing the broad-line wing emission, indicating that there are three outflows in motion. The integrated CO line intensity ratio (RICO(3-2)/ICO(2-1)) for the whole molecular arc is between 0.48 and 1.57. The maximum value is 1.57, which is much higher than previous measurements of individual Galactic MCs. The CO molecular arc has a line-intensity ratio gradient. The SNR G59.5+0.1 is in adiabatic expansion phase. The age of the SNR is 8.6x104yr. Based on the GLIMPSE I catalog, we select 625 YSOs candidates (including 176 Class I sources and 449 Class II sources). The timescales for Class 0, Class I and Class II sources are ≤104yr, ∼105yr, and ∼106yr, respectively. The number of YSOs are significantly enhanced in the interacting regions, indicating the presence of some recently formed stars.