Two words that are exceptions when they take possesive suffix ;

Su [water]  and Ne [what] appear in different form when they take possesive suffix ;

Su + y + um = Suyum [My water ] [ instead of "sum" ]

Su + y + un = Suyun [Your water ] [ instead of "sun" ]

Su + y + u =  Suyu [ His/Her/its water] [ instead of "susu" ]

etc.....

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Ne [what] + y + im --> Neyim [ what ......of me]

Ne [what] + y + in ---> Neyin [ what ......of you ]

Ne [what] + [y] + [s]i ---> Neyi [ what ......of he/she]

etc...

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Note : * For the word "Ne" the normal forms [ Nem, Nen, Nesi,Nemiz,Neniz,Neleri] are also acceptable however the exceptional forms [Neyim, Neyin, Neyi , Neyimiz,Neyiniz,Neleri] are used commonly.

As for su-y-* :

I wouldn´t say it´s an exception but historical development.

su < suw (< means older form. i.e. in old Turkish it was suw)

So

suy-um < suw-um

suy-un < suw-un

etc.

As for ne-si vs. ney-i; I had started a thread some time ago:

http://www.turkishclass.com/forumTitle_48291

There is a reason for every exception.

But your comment led us to some interesting information:

"Final /v/ sesi suvar-, sıva-, sıvık, sıvı vb. türevlerde korunmuştur." (Nişanyan Sözlük)

Here´s some more info Nişanyan Sözlük doesn´t mention:

"suw" is also present in Chinese languages (something like "shui"). It reminds us our distant common past with them.