Many people have been confused by the designation "Number exists***, **Death F" in the Father's Name Field in the Texas Birth Index.
I emailed the Texas Department of State Health Services and according to them:
This designation is actually **DEATH FILE NUMBER EXISTS***, and it means that the baby was deceased. At the time that the birth certificate was data entered, the only way to make the notation in the electronic record that the baby was deceased was to enter this in the father’s name fields. The actual birth certificate will show the name of the father if that information was available, and the birth certificate will be stamped "DECEASED."
This format is outdated, however, and no longer used.
Note: Several people have pointed out to me that Texas has made mistakes with this designation, so use good judgment and further research when you see this designation in the Index.