1, a 25c coin.
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3 dimes 13 nickles 5 pennies
The two coins are 10c and 25c. As stated in the question, one of them is not a quarter, if it's a leap year.
It is not possible to make 25 cents from 14 coins (US currency) There are only 1, 5, 10 and 25 cent coins Test: 14 x 1c = 14c, insufficient value 13 x 1c (=13) + 1 x 5c (=5) totals 18c, still not enough 12 x 1c (=12) + 2 x 5c (=10) totals 22c, still not enough. 11 x 1c (=11) + 3 x 5c (=15) totals 26c. Too much! If you use a 10c coin, you have to make the balance of 15c with 13 coins! Not possible! Of course, if you have 14 coins, which includes 10 x 1c (=10), and 3 x 5c (=15), you will easily make a total of exactly 25c, but only if you don't include the 14th coin!
The answer depends on the region whose currency the question is about. The US, for example has a 25 cent coin but not a 20 cent coin. The Euro, on the other hand, has a 20c coin but not 25c. I cannot guess what country you are interested in and so if you want a proper answer, you may want to specify the country.
$4.25c