A leap year starting on Monday is any year with 366 days (i.e. it includes 29 February) that begins on Monday, 1 January, and ends on Tuesday, 31 December. Its dominical letters hence are GF. The most recent year of such kind was 2024, and the next one will be 2052 in the Gregorian calendar[1] or, likewise, 2008 and 2036 in the obsolete Julian calendar.
Any leap year that starts on Monday has two Friday the 13ths: those two in this leap year occur in September and December. Common years starting on Tuesday share this characteristic.
Leap years that begin on Monday, along with those starting on Saturday and Thursday, occur least frequently: 13 out of 97 (≈ 13.4%) total leap years in a 400-year cycle of the Gregorian calendar. Their overall frequency is thus 3.25% (13 out of 400) of years.
Like all leap year types, the one starting with 1 January on a Monday occurs exactly once in a 28-year cycle in the Julian calendar, i.e. in 3.57% of years. As the Julian calendar repeats after 28 years that means it will also repeat after 700 years, i.e. 25 cycles. The year's position in the cycle is given by the formula ((year + 8) mod 28) + 1).