Exploring Reionization-era Quasars. III. Discovery of 16 Quasars at 6.4 ≲ <i>z</i> ≲ 6.9 with DESI Legacy Imaging Surveys and the UKIRT Hemisphere Survey and Quasar Luminosity Function at <i>z</i> ∼ 6.7

This is the third paper in a series aimed at finding reionization-era quasars with the combination of DESI Legacy imaging Surveys (DELS), the Pan-STARRS1 (PS1) Survey, and near-infrared imaging surveys, such as the UKIRT Hemisphere Survey (UHS), as well as the Wide-field Infrared Survey Explorer (WISE) mid-infrared survey. In this paper, we describe the updated quasar candidate selection procedure, report the discovery of 16 quasars at 6.4 less than or similar to z less than or similar to 6.9 from an area of similar to 13,020 deg(2), and present the quasar luminosity function (QLF) at z similar to 6.7. The measured QLF follows Phi(L-1450) proportional to L-1450(-2.35) in the magnitude range 27.6 < M-1450 < 25.5. We determine the quasar comoving spatial density at < z > - 6.7 and M-1450 < -26.0 to be 0.39 +/- 0.11 Gpc(-3) and find the exponential density evolution parameter to be k = -0.78 +/- 0.18 from z similar to 6 to z similar to 6.7, corresponding to a rapid decline by a factor of similar to 6 per unit redshift toward earlier epochs. This indicates that the rapid decline of quasar spatial density at z > 5 that was found by previous works continues to z > 6, at a rate significantly faster than the average decline rate between z similar to 3 and 5. We measured quasar comoving emissivity at z similar to 6.7, which indicates that high-redshift quasars are highly unlikely to make a significant contribution to hydrogen reionization. The broad absorption line quasar fraction at z greater than or similar to 6.5 is measured to be greater than or similar to 22%. In addition, we also report the discovery of six additional quasars at z similar to 6 in the Appendix.