The correct answer is option 3: ODI century. On New Year`s Day of 2014, Corey Anderson, a batsman from New Zealand, achieved the world record for the fastest ODI century. In One Day International (ODI) matches, a century refers to scoring 100 runs. This record-breaking achievement by Corey Anderson means that he reached the milestone of 100 runs in the shortest period of time compared to any other player in ODI history up until that point.

Let`s briefly explain the other options for better understanding. Option 1: Test century refers to scoring 100 runs in Test matches, which are the longest format of cricket. Option 2: Test fifty means scoring 50 runs in a Test match. Lastly, option 4: ODI fifty refers to scoring 50 runs in an ODI match.

It is important to note that the provided answer could be incorrect if the year or the specific match details are incorrect. In such a case, the correct answer should be alerted.