In this paper, we report the observed temporal correlation between extreme-ultraviolet (EUV) emission and magneto-acoustic oscillations in an EUV moss region, which is the footpoint region only connected by magnetic loops with million-degree plasma. The result is obtained from a detailed multi-wavelength data analysis of the region with the purpose of resolving fine-scale mass and energy flows that come from the photosphere, pass through the chromosphere and finally heat the solar transition region or the corona. The data set covers three atmospheric levels on the Sun, consisting of high-resolution broad-band imaging at TiO 7057 angstrom and the line of sight magnetograms for the photosphere, high-resolution narrow-band images at helium i 10830 angstrom for the chromosphere and EUV images at 171 angstrom for the corona. The 10830 angstrom narrow-band images and the TiO 7057 angstrom broad-band images are from a much earlier observation on 2012 July 22 with the 1.6 meter aperture Goode Solar Telescope (GST) at Big Bear Solar Observatory (BBSO) and the EUV 171 angstrom images and the magnetograms are from observations made by Atmospheric Imaging Assembly (AIA) or Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO). We report the following new phenomena: (1) Repeated injections of chromospheric material appearing as 10830 angstrom absorption are squirted out from inter-granular lanes with a period of similar to 5 minutes. (2) EUV emissions are found to be periodically modulated with similar periods of similar to 5 minutes. (3) Around the injection area where 10830 angstrom absorption is enhanced, both EUV emissions and strength of the magnetic field are remarkably stronger. (4) The peaks on the time profile of the EUV emissions are found to be in sync with oscillatory peaks of the stronger magnetic field in the region. These findings may give a series of strong evidences supporting the scenario that coronal heating is powered by magneto-acoustic waves.