That depends on what kind of database you have. If you have access to global variables or generators, just reset it each day and use it to seed your serial number column. If not, you can store the value in a table and look it up to seed your column, again resetting it each day.
Don't forget to increment the seeds manually if necessary. (Generators are a special kind of global variable that can auto-increment themselves if set up to do so. Other variables and certainly a record in a table do not.)
To reset the value, just set a trigger on insert that checks if COUNT(DATE = today)
is 0. If so, reset the value.