Why we don't say "at Monday"
What kind of error is it?

It is a grammatical error involving the incorrect use of the preposition "at" in time expressions. Specifically, "at" is incorrectly used before a day of the week, where "on" is the correct preposition in English.
Why do people make this mistake?
People may make this error due to confusion over which prepositions to use with different time expressions. "At" is used for specific times ('at 3 pm"), while "on" is used for days and dates ('on Monday", "on June 5th"). Non-native speakers might overgeneralize the use of "at" or be influenced by their native language structures.
What is correct?
The correct preposition to use before days of the week is "on", so the correct phrase is "on Monday".
Examples of correct usage
- I will start my new job on Monday.
- The meeting is scheduled on Thursday.
- We have a family dinner on Sunday.