Correct spelling, explanation: Saturday is a noun that originates from Middle English Saturdai. However, it came to English from the Latin translation of Sāturnī diēs, which means Saturn’s Day. That is why the correct spelling is Saturday and not Saterday. The mistake may be coming from phonetics because Saturday is pronounced as /ˈsæt ərˌdeɪ/, but it should not affect the written form and doesn’t make Saterday the right form.

Definition of Saturday:
noun: a day of the week after Friday and before Sunday;
I have signed up for the weekend ceramics classes and it starts next Saturday.
Our local drama club worked very hard on this play, we should go and see it, the premiere is on Saturday.

Incorrect spelling, explanation: Saterday is the misspelled version of the noun Saturday. Saturday originates from the translation of Latin Sāturnī diēs, which means Saturn’s Day. However, the current spelling is based on Middle English Saturdai. The reason for the mistaken form Saterday might be the phonetics because the pronunciation of Staurday is /ˈsæt ərˌdeɪ/ and it can cause the wrong spelling.