The point spread function (PSF) reflects states of a telescope and plays an important role in the development of data-processing methods, such as PSF-based astrometry, photometry, and image restoration. However, for wide field small aperture telescopes (WFSATs), estimating PSF in any position of the whole field of view is hard, because aberrations induced by the optical system are quite complex and the signal-to-noise ratio of star images is often too low for PSF estimation. In this paper, we further develop our deep neural network (DNN)-based PSF modelling method and show its applications in PSF estimation. During the telescope alignment and testing stage, our method collects system calibration data through modification of optical elements within engineering tolerances (tilting and decentring). Then, we use these data to train a DNN (Tel-Net). After training, the Tel-Net can estimate PSF in any field of view from several discretely sampled star images. We use both simulated and experimental data to test performance of our method. The results show that the Tel-Net can successfully reconstruct PSFs of WFSATs of any states and in any positions of the field of view (FoV). Its results are significantly more precise than results obtained by the compared classic method - inverse distance weight interpolation. Our method provides foundations for developing deep neural network-based data-processing methods for WFSATs, which require strong prior information of PSFs.