Serial Data type

The following documentation comment has been logged on the website:

Page: https://www.postgresql.org/docs/11/datatype-numeric.html
Description:

I read the doc at
https://www.postgresql.org/docs/11/datatype-numeric.html#DATATYPE-SERIAL. I
want to clarify how psql generate the sequence to existing data. Example if
I alter a table to add serial column so I will generate sequence value base
on integer to the existing data. So how did psql order in that case to
generate 1, 2, 3. Does it order by the created timestamp of the record or
the primary key of the table? is there a way to set the order when we alter
table?