We propose a theoretical model simulating ultrafast electron emission at the edge of a two-dimensional conducting sheet due to a strong field tunneling process in the presence of a static electric field. Under the assumption of a charge distribution following the square root law associated with a Sommerfeld half plane, the electric field was found to exhibit square-root dependence. The electron emission yield was estimated based on a Fowler-Nordheim tunneling, from which the resultant current flow was calculated by using the quasi-classical model. Importantly, we considered the number of the recoil electrons that do not contribute to the net current. We found a large variation in the nonlinearity of the power-dependence of the net field-emission yield; this is due to the combined contributions of the laser field irradiation and a static electric field. The validity of our model was confirmed based on experimental results obtained using devices with a nanometer-sized gap fabricated on a single layer of graphene.