A leap year starting on Saturday is any year with 366 days (i.e. it includes 29 February) that begins on Saturday, 1 January, and ends on Sunday, 31 December. Its dominical letter hence is BA, such as the years 1944, 1972, 2000, 2028, 2056, 2084, and 2124 in the Gregorian calendar or, likewise, 2012 and 2040 in the obsolete Julian calendar.
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Gregorian Calendar
Leap years that begin on Saturday, along with those starting on Monday, occur the least frequently - 13 out of 97 (≈ 13.4%) of all total leap years in a 400 year cycle. Their overall occurrence is 3.25%.
Trivia
A century leap year, that is the last year of a century and is also evenly divisible by 400, is always a leap year starting on Saturday and February 29 is always on Tuesday.
Julian Calendar
Like all leap year types, the one starting with 1 January on a Saturday occurs exactly once in a 28-year cycle in the Julian calendar, i.e. in 3.57% of years.
The final two digits of Julian years repeat after 700 years, i.e. 25 cycles.