The following use of apostrophe is correct.
Gita is Sita's sister.
But suppose Sita is name of two twin sisters and Gita is their younger sister. So how should we write that?
1) Gita is Sitas' sister.
Or
2) Gita is Sita's sister.
It seems to me, that in certain cases, the apostrophe comes after the s, though I might be wrong.
You are kind of right.
The apostrophe comes after the "s" when the "s" is part of the word. This includes plurals ("the dogs' bone") as well as non-plurals that happen to end in "s", eg, "Mr Davis' daughter", "the bass' strings" (as in, a bass guitar).
The problem is that, in English (I don't know about other languages/cultures), you would generally not have sisters with the same name - if you did, you would have to explain that in your answer. So in this particular instance, while "Gita is Sitas' sister" is grammatically correct, your exact meaning would not be understood without the extra information, which in most cases would be done with rephrasing: eg, you could say "Gita is the sister of the Sitas (they are twins with the same name)". If the person to whom you are speaking already knows of the unusual case of the twins with the same name, then they probably would understand "Gita is the Sitas' sister" (you would need to add "the" to avoid confusion with "Sita's" singular).
As an aside, you may sometimes see " 's" after an "s", as in "Mr Davis's daughter". This is the same as just the apostrophe ("Mr Davis' daughter"), but old-fashioned use.
