In the books and literature following the Game of Thrones universe a knight's title is spelt with an 'e' not an 'i' for "Ser". Why is this?
George RR Martin has a penchant for introducing things in his universe which resemble those in ours, yet have a different texture to them. This lets the user relate to those "words" better and at the same time renders them an exotic and enigmatic aura.
That's the reason Sir becomes Ser, Master becomes Maester. The same can also be observed in the way he names people. Rob is Robb and Edward is Eddard.
All these are mere ploys to create an enchanting but understandable world!
Ser is used in other fantasy works as well. It's a gender neutral title. It's possible ser is an older version of sir (like many words that have changed over time) so ser would be the correct spelling for the period.
You can also google search to find the many different works that use 'Ser'. Just think, "Old English".