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The fiducial cosmological analyses of imaging galaxy surveys like the DarkEnergy Survey (DES) typically probe the Universe at redshifts $z < 1$. This ismainly because of the limited depth of these surveys, and also because suchanalyses rely heavily on galaxy lensing, which is more efficient at lowredshifts. In this work we present the selection and characterization ofhigh-redshift galaxy samples using DES Year 3 data, and the analysis of theirgalaxy clustering measurements. In particular, we use galaxies that are fainterthan those used in the previous DES Year 3 analyses and a Bayesian redshiftscheme to define three tomographic bins with mean redshifts around $z \sim0.9$, $1.2$ and $1.5$, which significantly extend the redshift coverage of thefiducial DES Year 3 analysis. These samples contain a total of about 9 milliongalaxies, and their galaxy density is more than 2 times higher than those inthe DES Year 3 fiducial case. We characterize the redshift uncertainties of thesamples, including the usage of various spectroscopic and high-quality redshiftsamples, and we develop a machine-learning method to correct for correlationsbetween galaxy density and survey observing conditions. The analysis of galaxyclustering measurements, with a total signal-to-noise $S/N \sim 70$ after scalecuts, yields robust cosmological constraints on a combination of the fractionof matter in the Universe $\Omega_m$ and the Hubble parameter $h$, $\Omega_m h= 0.195^{+0.023}_{-0.018}$, and 2-3% measurements of the amplitude of thegalaxy clustering signals, probing galaxy bias and the amplitude of matterfluctuations, $b \sigma_8$. A companion paper $\textit{(in preparation)}$ willpresent the cross-correlations of these high-$z$ samples with CMB lensing fromPlanck and SPT, and the cosmological analysis of those measurements incombination with the galaxy clustering presented in this work.

The Dark Energy Survey Year 3 high redshift sample: Selection, characterization and analysis of galaxy clustering