What is the Christian's Day ?

Christians always worshipped on the first day (Sunday), They called the first day (Sunday) the Lord's day .

Sunday is Sun+day , literally meaning "sun's day"

The official sun god of the later Roman Empire was "Sol Invictus" "Birthday of Sol Invictus" was December 25th.

The Christians celebrate the same day as birthday of Jesus (who is considered as God) and celebrate the Sunday as Christian's day