We investigated the spontaneous deformation and fission of a tetradecane droplet containing palmitic acid (PA) on a stearyltrimethylammonium chloride (STAC) aqueous solution. In this system, the generation and rupture of the gel layer composed of PA and STAC induce the droplet deformation and fission.To investigate the characteristics of the droplet-fission dynamics, we obtained the time series of the number of the droplets, and confirmed that the number has a peak at a certain STAC concentration. Since the fission of the droplet should be led by the deformation, we analyzed four parameters which may relate to the fission dynamics from the spatio-temporal correlation of the droplet-boundary velocity. As a result, we found that the faster deformation would be the key factor for the fission dynamics.