If sistren is the female equivalent of brethren, what is the female equivalent of fellow? Words usually paired are: guy/gal; man/woman; boy/girl; lad/lass; brethren/sistren; fraternity/sorority; but I have seen nothing for fellow.
According to Etymology Online, fellow has been:
Used familiarly since mid-15c. for "man, male person," but not etymologically masculine.
It would be perfectly acceptable to call a woman a fellow traveler, for instance.
A similarly toned word for a woman, but not related to fellow, might be simply lady, or woman, as in, "my dear lady...".
I think you could conceivably get away with using "fellow" for a woman. ("For she's a jolly good fellow!", although that may be limited to the context of the song.) If you want a word with the same sort of archaic feel as fellow, "chapess" might do the job, although it's both colloquial, and a neologism, as was as being more obviously paired with "chap".
Either girl or gal, depending on age of the subject and the context, would carry about the same air of casualness as fellow.
You son is a cute little fellow. Your daughter is a cute little gal.
Who's that fellow over there? And who's the girl with him?
If she is stuck in the 1950's and calling her boyfriend her fellow, those words would work for what he would call her, too. If she is a fellow in the collegiate sense, she is of course a fellow.
Sorry, but I can't come up with a unique form of fellow that is not already paired with one of the others. I wonder if it's a holdover from the era when women were treated with more respect (in polite society, and in public, at least), and so there's a dearth of casual yet respectable words for women from that time. (I may be wrong about the use of fellow elsewhere, but in general I only hear older people using the word).
I have heard the expression "every fellow needs a filly". It's originally used to refer to a female horse but has a less common informal meaning that's comparable to fellow.
The word you are looking for is "sheila"
N.B., this answer was edited.