Efficient preparation of cold atoms plays an important role in the precision measurement including optical lattice clocks (OLCs). Fast preparation of cold atoms reduces Dick noise by shortening dead time in a clock interrogation cycle, which improves the stability of OLCs. Here, we increase the loading rate of the three-dimensional magneto-optical trap (3D-MOT) in the ultra-high vacuum environment by utilizing the two-dimensional magneto-optical trap (2D-MOT) with a push beam, reduce the temperature of cold atoms with the compressing-MOT technique which is implemented by decreasing the detuning of 3D-MOT rapidly at the end of atom preparation, and realize the enhanced production of cold atoms for <sup>199</sup>Hg OLCs. To achieve 3D-MOT and 2D-MOT of mercury atoms, a deep ultraviolet laser (DUVL) system composed of three DUVLs is developed with one working in lower power for frequency locking and the other two in high power for laser cooling. Such configuration improves the long-term frequency stability and shows greater robustness than our previous system consisting of two DUVLs. To maximize the 3D-MOT loading rate, we orderly optimize the detuning and the magnetic field gradient of 3D-MOT and those of 2D-MOT as well as the detuning and the power of the push beam. After the optimization of all parameters, we measure the maximum loading rate of 3D-MOT to be 3.1×10<sup>5</sup>/s and prepare cold atoms of 1.8×10<sup>6</sup> in 9 s. The loading rate is greatly enhanced by a factor of 51 with 2D-MOT and the push beam. To improve the efficiency that cold atoms transfer from 3D-MOT to optical lattice, we use the compressing-MOT technique to reduce the temperature of cold atoms and produce cold <sup>199</sup>Hg atoms of about 45 μK, below the temperature expected by Doppler cooling theory. By achieving the high gain of the 3D-MOT loading rate under the ultra-high vacuum and reducing the temperature of cold atoms, this enhanced preparation of cold atoms based on 2D-MOT effectively shortens the preparation time of cold atoms and improves the transfer efficiency of optical lattice, which provides a significant scheme for the efficient preparation of cold mercury atoms in other experiments.