A significant limitation of current smartphone-based eye-tracking algorithms is their low accuracy when applied to video-type visual stimuli, as they are typically trained on static images. Also, the increasing demand for real-time interactive applications like games, VR, and AR on smartphones requires overcoming the limitations posed by resource constraints such as limited computational power, battery life, and network bandwidth. Therefore, we developed two new smartphone eye-tracking techniques for video-type visuals by combining Convolutional Neural Networks (CNN) with two different Recurrent Neural Networks (RNN), namely Long Short Term Memory (LSTM) and Gated Recurrent Unit (GRU). Our CNN+LSTM and CNN+GRU models achieved an average Root Mean Square Error of 0.955cm and 1.091cm, respectively. To address the computational constraints of smartphones, we developed an edge intelligence architecture to enhance the performance of smartphone-based eye tracking. We applied various optimisation methods like quantisation and pruning to deep learning models for better energy, CPU, and memory usage on edge devices, focusing on real-time processing. Using model quantisation, the model inference time in the CNN+LSTM and CNN+GRU models was reduced by 21.72% and 19.50%, respectively, on edge devices.