What is the most Executive Orders signed by a US President in a single four year term and whom was it?
Franklin D. Roosevelt definitely had the most overall at 3522. FDR averaged 290.8 per year, which is also the highest rate (comparable in magnitude in one year to the 291 and 275 that George W. Bush and Barack Obama had in their eight years respectively).
For a single four-year term, Roosevelt's first term (1933-1936) had at least 1715. Some of the 253 in 1937 may have been in the first term as well, as it lasted until noon on January 20th, 1937.
Only Woodrow Wilson (1803 in 8 years) had more than 1715 executive orders total. It would be barely possible that almost all of those were in one term but unlikely. The source doesn't break down Wilson's orders by year, but it does list an order 1888 from 1914 and 2859 from 1918. Working backward, from Herbert Hoover's first order (5075) gives Wilson as ranging from 1547 to 3349. Even assuming no other executive orders, that doesn't allow for enough in either term. So unless there's a problem with the numbering, Wilson had fewer than 1715 in each term.
TL;DR Most likely Franklin D. Roosevelt with at least 1715.
FDR had 3,522 over 3 terms which averages to 1174 per term.
That's not necessarily the most for one term but he was so far ahead of any other president that it doesn't look like there are any other contenders.
There is a table of orders per year.
Franklin D. Roosevelt - 290.8
Herbert Hoover - 242
Woodrow Wilson - 225.4
Warren G. Harding - 216.9
Calvin Cooledge - 215.2
William Howard Taft - 181
Theodore Roosevelt - 144.7
Harry S. Truman - 116.7
All the other presidents had less than 100 per year.
Note that Donald J. Trump had signed 12 at the time the article was updated, but that cannot be extrapolated to the end of the year at the same rate. If it could be it would come to 285.7