I believe that Luther Fiske the son of Bezaleel Fiske and Rebeckah Rand and Azubah Pierce daughter of Josiah Pierce and Sarah Gale, are the parents of Catherine Fiske.
So far all I have is supposition but there are several things going on that would cause confusion and several things that bear this out.
Here is what I believe. (Some of this I hope to be able to prove and some I already can.)
abt 1783 Azubah Pierce married Luther Fiske in Worcester Co., Massachusetts (Probably the city of Worcester.)
30 July 1784 Luther Fiske and Azubah _____ had a daughter, Kata Fiske (aka Catherine Fiske).
abt 1784 or 1785 Luther Fiske died. (Probably in Worcester Co., Massachusetts)
15 May 1786 Azubah Fisk married Amherst Morse in Boylston, Worcester Co., Masachusetts.
1790 Amherst Morse resides in Boylston Ma with two females at the time of the 1790 Federal Census.
1814 Catherine Fiske opens the Seminary for Girls in Keene, Cheshire Co., New Hampshire.
20 May 1837 Catherine Fiske died in Keene, New Hampshire.
9 November 1837 Azubah Morse died in Keene, New Hampshire and is buried in the same plot as her daughter, Catherine Fiske. (I believe plot 181.)
Much of the confusion is caused by there being at least two Luther Fisk(e)s marrying two different Azubahs in Worcester Co., Ma. between 1783 and 1804. And two different Azubah Fisks marrying two different men in Worcester Co., Massachusetts between 1786 and 1787.
Again, this is all conjecture but if anyone can give me proof to either prove out or dismiss this information I would love to see it.