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Context.The determination of accurate photometric redshifts (photo-zs) in large imaging galaxy surveys is key for cosmological studies. One of the most common approaches is machine learning techniques. These methods require a spectroscopic or reference sample to train the algorithms. Attention has to be paid to the quality and properties of these samples since they are key factors in the estimation of reliable photo-zs. Aims.The goal of this work is to calculate the photo-zsfor the Year 3 (Y3) Dark Energy Survey (DES) Deep Fields catalogue using the Directional Neighborhood Fitting (DNF) machine learning algorithm. Moreover, we want to develop techniques to assess the incompleteness of the training sample and metrics to study how incompleteness affects the quality of photometric redshifts. Finally, we are interested in comparing the performance obtained by DNF on the Y3 DES Deep Fields catalogue with that of the EAzY template fitting approach. Methods.We emulated – at a brighter magnitude – the training incompleteness with a spectroscopic sample whose redshifts are known to have a measurable view of the problem. We used a principal component analysis to graphically assess the incompleteness and relate it with the performance parameters provided by DNF. Finally, we applied the results on the incompleteness to the photo-zcomputation on the Y3 DES Deep Fields with DNF and estimated its performance. Results.The photo-zsof the galaxies in the DES deep fields were computed with the DNF algorithm and added to the Y3 DES Deep Fields catalogue. We have developed some techniques to evaluate the performance in the absence of “true” redshift and to assess the completeness. We have studied the tradeoff in the training sample between the highest spectroscopic redshift quality versus completeness. We found some advantages in relaxing the highest-quality spectroscopic redshift requirements at fainter magnitudes in favour of completeness. The results achieved by DNF on the Y3 Deep Fields are competitive with the ones provided by EAzY, showing notable stability at high redshifts. It should be noted that the good results obtained by DNF in the estimation of photo-zsin deep field catalogues make DNF suitable for the future Legacy Survey of Space and Time (LSST) andEucliddata, which will have similar depths to the Y3 DES Deep Fields.