Obtaining a prize postdoctoral fellowship in astronomy and astrophysics involves a number of factors, many of which cannot be quantified. One criterion that can be measured is the publication record of an applicant. The publication records of past fellowship recipients may, therefore, provide some quantitative guidance for future prospective applicants. We investigated the publication patterns of recipients of the NASA prize postdoctoral fellowships in the Hubble, Einstein, and Sagan programs from 2014 through 2017, using the NASA ADS reference system. We tabulated their publications at the point where fellowship applications were submitted, and we find that the 133 fellowship recipients in that time frame had a median of 6 +/- 2 first-author publications, and 14 +/- 6 co-authored publications. The full range of first author papers is 1 to 15, and for all papers ranges from 2 to 76, indicating very diverse publication patterns. Thus, while fellowship recipients generally have strong publication records, the distribution of both first-author and co-authored papers is quite broad; there is no apparent threshold of publications necessary to obtain these fellowships. We also examined the post-PhD publication rates for each of the three fellowship programs, between male and female recipients, across the four years of the analysis and find no consistent trends. We hope that these findings will prove a useful reference to future junior scientists.