Indexing Irish Baptism records 1831. What does the "F" mean?
Example: Sarah Anna Tale F Eugenii & Rose Flanigan
Another example: Rosa Rice F Jacobi & Marie King
Most records are in this format: Mary Anne of Michael and Bridget Jennings
Are "Tale" and "Rice middle names or surnames?
The f could perhaps be an abbreviation for the Latin word filia meaning daughter.
The other words may be names as you suggest, or perhaps could also be Latin words, or Latin abbreviations. Could you post a screen shot, (for each) which may give more clues.
Latin Genealogical Word List https://www.familysearch.org/en/wiki/Latin_Genealogical_Word_List FamilySearch Wiki0
I am wondering if the person being baptized is an adult and the name following the "F" is the church pastor, since that name is always in latin.0
Most likely that f. is an abbreviation for filius (son) and filia (daughter)
It is quite common for Latin to be used in Catholic records.
The example above:
Sarah Anna Tale F Eugenii & Rose Flanigan
Sarah Anna Tale daughter of Eugenius [Tale] and Rose Flanigan.
Note that endings. Latin is a declined language. When the "us" on the end of the name is changed to "i" it becomes the possessive form, i.e Eugneii = of Eugenius.2