Sunday.
Consider this. Start on January 9th, and count back the years and leap days (12), and you have 16859 days. 16859 mod 7 = 3, and 9 - 3 = 6, and the 6th was a Wednesday.
January 6th, 1900 was a Saturday.
January 6th, 1862 fell on a Monday.
January 6th, 1993 fell on a Wednesday.
January 6th, 1954 fell on a Wednesday.
Friday
January 6, 1955 was a Thursday.
Thursday
Friday
6th October 1968 was a Sunday.
April 6th 1952 was a Sunday.
July 6th 1990 was a Friday.