Aaaah. This will be much easier to help now!
First, there is a specific word for "some" in Turkish in that sense. It is "birkaç" and this is not used.
Indefinite possessive structures are always made using genitive and var. Definite ones are formed with the locative construction like this! :)
"Genç filler onda." Translation: She has the young elephants.
Is "Genç filleri onda" wrong for "she has the young elephants"?
Yes it is wrong & I will explain why.
The question is asked in Turkish & there is no (accusative) case suffix "-i" after the plural suffix in elephants.
Fil + "-ler" --> elephants.
Genç filler --> the young elephants.
O --> he/she/it. O + (n) buffer + "-da" (locative) case suffix for "onda."
Why did you change the Turkish question? & how did you determine the need to use the accusative case suffix?