Daha hızlısı yok.

What does the above phrase mean?

Possessive -(s)i after an adjective? That seems odd to me...

The above satement can be a short form of the following  satement:

"Bunun daha hızlısı yok." In this statement, the word "hızlısı" isn´t used as an adjective but as a noun. (When an adjective doesn´t describe a noun and is used without a noun, we can´t call it as an adjective anymore, because it becomes a noun. In Turkish grammar, it is called as "adlaşmış sıfat")

Let´s look at the following examples:

In the first sentences, the word "çalışkan" is used as adjectice, but in the second sentences as noun".

Çalışkan insanları severim - Çalışkanları severim

Sınıfın en çalışkan öğrencisi, Ali´dir - Sınıfın en çalışkanı, Ali´dir. 

I hope the explanation will be useful.

 I am always getting words reversed  so can you tell me

daha hızsılı yok

does it mean:

not only faster

or

still not faster

I think we can say that "There isn´t any faster than this one."

or

"This is the fastest one of all models."

thank you

You are welcome...

Thank you for help

So, may the phrase be considered to be a synonym to bundan (daha) hızlı yok?

Or such a construction is incorrect?

I found a sentence with a little bit similar structure.

Onun kadar sanata önem veren bir ikincisi yoktu. ’There wasn’t another one who cared about art like him.’

(bir ikincisi literally ‘a second-of-his’ just like in your example daha hızlısı ‘quicker-of-his’ )

I mean if you are interested.

"bir ikincisi" is the short form of "bir ikinci kişi". (Onun kadar sanata önem veren ikinci bir kişi yoktu.)

In "ikinci kişi", "ikinci" is adjective. In the short form (bir ikincisi), the noun (kişi) is dropped and the adjective (ikinci) becomes noun and accepts the suffix "(s)ı". (As I have explained in my previous post.)

One of the secret recipes in Turkish syntax is the lack of a strict distinction between nouns and adjectives. It just takes some time before someone with Latin grammar background understands it.