Hello! So, İ want to ask this question. İ understand the meaning of the phrase, but what is the exact grammar behind it? İ can´t really make sense of the grammar. For example İ know ´neyim´ is what am İ, but for 2nd person İ know it´s ´nesin´, so what is ´neyin´ then? Yani birisi edebilir mi? Şimdiden çok teşekkür ederiz!

I think it´s possessive but an irregular spelling. 

http://www.turkishclass.com/forumTitle_54203

I would suggest that it´s genitive case. (-ın,-in,-un,-ün; -nın,-nin,-nun,-nün)

Only these two words, ne and su, do not follow the rule.

According to the rule they are expected to be formed as ne.nin and su.nun.

But, however, as if they end in a vowel, instead of -nin and -nun, they take -in and -un with the helping letter -y : ne.y.in, su.y.un

Here are some examples: "neyin kafası, neyin nesi, neyin üstü, suyun dibi, suyun rengi"

It is the same with the possessive (3rd.per.sing.-ı,-i,-u,-ü;-sı,-si,-su,-sü

su.y.u instead of su.su

but both ne.y.i and ne.si are possible:

neyi var? <=> nesi var?