The flow phenomena around a rotating elliptic cylinder placed in a narrow channel is studied numerically. The walls of the channel act as a confinement that limits the flow in the transverse direction. The confinement ratio (β), non-dimensional rotation rate (α), and the Reynolds number (Re) span across multiple values. A parametric study is done to identify the variations in drag-coefficient (CD), lift-coefficient (CL), and moment coefficient (CM) with changes in β,α and Re. Near-field and far-field vorticity contours are discussed in detail. Fast Fourier transform (FFT) of the time-periodic lift signals are presented to understand the shedding-frequency characteristics. Furthermore, CM values are analysed for possible cases of autorotation. It is observed that confinement acts to delay the shedding of vortices. However, a complete suppression is not obtained even for the maximum value of β. This is likely because of the sharp flow separation at the edges of the cylinder, which tends to promote the formation of a vortex. Hovering vortices are observed for α>1, and a special case is identified for which the hovering vortex never dissipates.