Hope this isn't a field being used as a primary key.
You can set up a script that runs once a day or each time that the file is opened. The script can check a field in a single record in a separate file for the year the serial number was last reset. If Year ( Get ( CurrentDate ) ) does not equal that value, use the "Set Next Serial Value" script step to set the value back to zero. Then update this field to show that the serial number as been reset for the current year so that the next time the script runs, it does nothing.
Slightly different question:
How to set a serial number whose first four digits follow the year, and the last four keep growing, so it can be a key:
For 2014, on Jan 1, first number is 20140001, last number on Dec 31st is 20140135
For 2015, on Jan 1, first number is 20150136, last number on Dec 31st is 20150259, or wherever it ends.
To repeat, such a field should not be used as a Primary key to match records in relationships.
I'd use one field for the year and one for the auto-entered serial number. Merge fields on a layout can combine the two to produce what looks like a seamless value or a calculation field can combine them into a single value.