There was no year zero, so there is no answer to the question if that is what you mean. If you meant 2000, then the 1st of January 2000 was on a Saturday.
January 1 2010 will be a Friday.
January 1 1974 was a Tuesday.
1 January 1994 was a Saturday.
January 1 1979 was on a Monday.
1 January 1970 was a Thursday.
1 January 2014 will be a Wednesday.
1 January 2006 was a Sunday.
1 January 1975 was a Wednesday.
1 January 1986 was a Wednesday.
1 January 2017 will be a Sunday.
1 January 2005 was a Saturday.
January 1, 1950 was on a Sunday.