Step-by-step Solution:

\[ \textbf{Step 1: From 1st January 2022 to 1st January 2023 is exactly one year.} \] \[ \textbf{Step 2:Since 2022 is not a leap year (it has 365 days), the number of days between the two dates is 365.} \] \[ \textbf{Step 3: 365 / 7 = 52 weeks and 1 extra day.} \] \[ \textbf{Step 4: Therefore, 1st January 2023 will be 1 day ahead of 1st January 2022.} \] \[ \text{Since 1st January 2022 was Saturday, 1st January 2023 will be Sunday.} \] \[ \textbf{Final Answer: } \boxed{\text{Sunday}} \]